It is because amplitude of your `Sin` function is very small relative to the length of its arc (you picked `0.001 Sin[x]`), so it looks almost flat when you rotate it. You can see it non-flat initially because Mathematica auto-rescales Y-axes to zoom in on your small amplitude. When you rotate by Pi/3 curve that is Pi-long in base, its end lifts by `Pi Tan[Pi/3]` or `N[Pi Sqrt[3]]` or ~ 5.4414. Relative to this hight .001 will not bee seen. You can see that there is nothing wrong with rotation if you pick amplitude comparable to the length arc:

    fig0=Plot[Sin[x],{x,0,Pi},Axes->False];
    Manipulate[
    	Graphics[
    		GeometricTransformation[fig0[[1]],RotationTransform[r]],
    	Frame->True,Axes->True,PlotRange->3],
    {r,0,2Pi}]

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/C0lI1.gif