2D Registration of two shapes

Question

I am having a task to implement a way of registration of two 2D Shapes. The first shape is the source, meaning it will never change, and the target shape is the shape that must be always aligned/registered on the source shape. For both shapes I have the X,Y coordinates.

In order to understand the problem, I'm adding a photo that explains it.

The Angle of the rotation of Red shape is unknown and cannot be for every random red shape the same. So I need an algorithm to find the best rotation in order to match the blue shape.

Any ideas?? I've read about ICP but does it work for 2D problems? Because I used an implementation but for the 2D data it never converged, but for 3D data I found was working perfectly.

Thanks in advance,