The Solar Ring would have two spins in relation to the Earth: a slow heliostatic spin of one rotation per year to face the sun and a latitudinal orbit that varies according to the size of the ring, which would keep the ring in position. The ring would be orbiting at around 30,000 km, just below the High Earth Orbit. The ring would require an air space of 10-20 km to itself, depending on it's size, in order to avoid collisions with stray satellites.

More information about orbits in general can be found here.