Cfrgtkky

With the help of the new library angles of TikZ 3.0.0 and a small patch, it is possible to get:

thanks to:

begin{tikzpicture}

draw  ( 0 , 0 ) coordinate (A) 

    -- ( 4 , 0 ) coordinate (C) 

    -- ( 0 , 3 ) coordinate (B) 

    -- ( 0 , 0 )

    pic [draw,blue,thick,angle radius=0.5cm]  {squared angle = A--C--B}

    pic [draw,red,thick,angle radius=0.5cm]   {squared angle = C--A--B}

    pic [draw,green,thick,angle radius=0.5cm] {squared angle = C--B--A};

    ;

end{tikzpicture}

The complete code:

documentclass[tikz,border=10pt]{standalone}

usepackage{tikz}

usetikzlibrary{angles}



makeatletter

tikzset{

  pics/squared angle/.style = {

    setup code  = tikz@lib@angle@parse#1pgf@stop,

    background code = tikz@lib@angle@background#1pgf@stop,

    foreground code = tikz@lib@squaredangle@foreground#1pgf@stop,  

  },

  pics/squared angle/.default=A--B--C,

  angle eccentricity/.initial=.6,

  angle radius/.initial=5mm

}



deftikz@lib@squaredangle@foreground#1--#2--#3pgf@stop{%

  path [name prefix ..] [pic actions]

  ([shift={(tikz@start@angle@temp:tikz@lib@angle@rad pt)}]#2.center)

    |-

  ([shift={(tikz@end@angle@temp:tikz@lib@angle@rad pt)}]#2.center);

  ifxtikzpictextrelaxelse%

    defpgf@temp{node()[name prefix

      ..,at={([shift={({.5*tikz@start@angle@temp+.5*tikz@end@angle@temp}:pgfkeysvalueof{/tikz/angle

            eccentricity}*tikz@lib@angle@rad pt)}]#2.center)}]}

    expandafterpgf@tempexpandafter[tikzpictextoptions]{tikzpictext};%

  fi

}

makeatother



begin{document}

begin{tikzpicture}

draw  ( 0 , 0 ) coordinate (A) 

    -- ( 4 , 0 ) coordinate (C) 

    -- ( 0 , 3 ) coordinate (B) 

    -- ( 0 , 0 )

    pic [draw,blue,thick,angle radius=0.5cm]  {squared angle = A--C--B}

    pic [draw,red,thick,angle radius=0.5cm]   {squared angle = C--A--B}

    pic [draw,green,thick,angle radius=0.5cm] {squared angle = C--B--A};

    ;

end{tikzpicture}

end{document}

The desired output seems to have the box filled in red as well as a label, hence let's use the quotes library:

documentclass[tikz,border=10pt]{standalone}

usepackage{tikz}

usetikzlibrary{angles,quotes}



makeatletter

tikzset{

  pics/squared angle/.style = {

    setup code  = tikz@lib@angle@parse#1pgf@stop,

    background code = tikz@lib@angle@background#1pgf@stop,

    foreground code = tikz@lib@squaredangle@foreground#1pgf@stop,  

  },

  pics/squared angle/.default=A--B--C,

  angle eccentricity/.initial=.6,

  angle radius/.initial=5mm

}



deftikz@lib@squaredangle@foreground#1--#2--#3pgf@stop{%

  path [name prefix ..] [pic actions]

  ([shift={(tikz@start@angle@temp:tikz@lib@angle@rad pt)}]#2.center)

    |-

  ([shift={(tikz@end@angle@temp:tikz@lib@angle@rad pt)}]#2.center);

  ifxtikzpictextrelaxelse%

    defpgf@temp{node()[name prefix

      ..,at={([shift={({.5*tikz@start@angle@temp+.5*tikz@end@angle@temp}:pgfkeysvalueof{/tikz/angle

            eccentricity}*tikz@lib@angle@rad pt)}]#2.center)}]}

    expandafterpgf@tempexpandafter[tikzpictextoptions]{tikzpictext};%

  fi

}

makeatother



begin{document}

begin{tikzpicture}

draw  ( 0 , 0 ) coordinate (A) 

    -- ( 4 , 0 ) coordinate (C) 

    -- ( 0 , 3 ) coordinate (B) 

    -- ( 0 , 0 )

    pic [draw,fill=red,angle radius=0.5cm,angle eccentricity=2,

    "$90^circ$" {black,font=footnotesize}]   {squared angle = C--A--B}

    ;

end{tikzpicture}

end{document}

The result:

For this simple case, you can just draw a square at (A):

documentclass[tikz,border=10pt]{standalone}

begin{document}

begin{tikzpicture}

draw  ( 0 , 0 ) coordinate (A)

    -- ( 4 , 0 ) coordinate (C)

    -- ( 0 , 3 ) coordinate (B)

    -- (0,  0);

draw [fill=red](A) rectangle ++(0.5,0.5) node[above right]{$90^circ$};

end{tikzpicture}

end{document}

This is an approach simplified by »tkz-euclide«, which is mentioned indirectly in the comment to your question. Wherever the points are located that define the triangle, the right angle will be marked automatically.

documentclass[11pt]{article}

usepackage[T1]{fontenc}

usepackage{tkz-euclide}

usetkzobj{all}



begin{document}

  begin{tikzpicture}

    tkzDefPoint(0,0){A}

    tkzDefPoint(0,3){B}

    tkzDefPoint(4,0){C}

    tkzMarkRightAngle[draw=red,fill=red](B,A,C)

    tkzDrawPolygon(A,B,C)

  end{tikzpicture}

end{document}

For details please refer to the package manual, which is unfortunately only available in French.

This is how. Take the (A) as your reference point. Then (1) yshift to move the starting point up a little; (2) xshift to determine the end point; (3) connect these two points using -| (going horizontally and then vertically to the end point.)

documentclass{minimal}

usepackage{tikz}

begin{document}

begin{tikzpicture}

draw  ( 0 , 0 ) coordinate (A) 

    -- ( 4 , 0 ) coordinate (C) 

    -- ( 0 , 3 ) coordinate (B) 

    -- (0,  0);

%draw [red]([yshift=0.5cm]A) -| node[above right]{$90^circ$}; % generates red line

draw [fill=red]([yshift=0.5cm]A) -| node[above right]{$90^circ$} ([xshift=0.5cm]A) 

-- (A) -- cycle ;   % if path is used, the square becomes invisible.

end{tikzpicture}

end{document}

With PSTricks.

documentclass[pstricks,border=12pt,12pt]{standalone}

usepackage{pst-eucl}

begin{document}

begin{pspicture}(6,6)

    pstGeonode[CurveType=polygon,PosAngle={-90,0,90}](1,1){A}(5,1){B}(1,5){C}

    pstRightAngle[fillstyle=solid,fillcolor=red]{B}{A}{C}

end{pspicture}

end{document}

Note : Since version 3.1 of TikZ right angle is part of the standard angles library. It works in the same way as angle pic.

This answer is very close to the answer of @ClaudioFiandrino, which is a slight modification of the standard angles library.

documentclass[tikz,border=7pt]{standalone}

usetikzlibrary{angles, quotes}



makeatletter

tikzset{

  pics/right angle/.style = {

    setup code  = tikz@lib@angle@parse#1pgf@stop,

    background code = tikz@lib@rightangle@background#1pgf@stop,

    foreground code = tikz@lib@rightangle@foreground#1pgf@stop,

  },

  pics/right angle/.default=A--B--C,

  angle eccentricity/.initial=.6,

  angle radius/.initial=5mm

}



deftikz@lib@rightangle@background#1--#2--#3pgf@stop{%

  path [name prefix ..] [pic actions, draw=none] (#2.center)

    -- ++(tikz@start@angle@temp:tikz@lib@angle@rad pt)

    -- ++(tikz@end@angle@temp:tikz@lib@angle@rad pt)

    -- ++(tikz@start@angle@temp:-tikz@lib@angle@rad pt)

    -- cycle;

}



deftikz@lib@rightangle@foreground#1--#2--#3pgf@stop{%

  path [name prefix ..] [pic actions, fill=none, shade=none]

  ([shift={(tikz@start@angle@temp:tikz@lib@angle@rad pt)}]#2.center)

  -- ++(tikz@end@angle@temp:tikz@lib@angle@rad pt)

  -- ++(tikz@start@angle@temp:-tikz@lib@angle@rad pt);

  ifxtikzpictextrelaxelse%

    defpgf@temp{node()[name prefix

      ..,at={([shift={({.5*tikz@start@angle@temp+.5*tikz@end@angle@temp}:pgfkeysvalueof{/tikz/angle

            eccentricity}*sqrt(1/2)*tikz@lib@angle@rad pt)}]#2.center)}]}

    expandafterpgf@tempexpandafter[tikzpictextoptions]{tikzpictext};%

  fi

}

makeatother



begin{document}

  begin{tikzpicture}

    draw  (4,1) coordinate (C)

        -- (0,0) coordinate (A)

        -- ([turn] 0,3) coordinate (B)

        -- cycle

        pic [draw,red,"$cdot$",angle eccentricity=.5]   {right angle = B--A--C}

        pic [draw,blue,thick]  {right angle = A--C--B}

        pic [fill=green,draw] {right angle = C--B--A};

        ;

  end{tikzpicture}

end{document}

Note : I have created a rightangles library, available at GitHub that can be used in place of this hack like this

documentclass[tikz,border=7pt]{standalone}

usetikzlibrary{rightangles, quotes}



begin{document}

  begin{tikzpicture}

    draw  (4,1) coordinate (C)

        -- (0,0) coordinate (A)

        -- ([turn] 0,3) coordinate (B)

        -- cycle

        pic [draw,red,"$cdot$",angle eccentricity=.5]   {right angle = B--A--C}

        pic [draw,blue,thick]  {right angle = A--C--B}

        pic [fill=green,draw] {right angle = C--B--A};

        ;

  end{tikzpicture}

end{document}