Building the ring would be interesting engineering challenge. Once you build it with sun in its center of mass, it's in unstable equilibrium, so you only need t

Building the ring would be interesting engineering challenge. Once you build it with sun in its center of mass, it's in unstable equilibrium, so you only need to compensate for the drift. But until it is built, your components have to orbit the sun. So the finished ring would also keep this momentum and it would be rotating around its center.