Aside from what Rubidium noted, a few discussions about it online for you:Erm it should still hold an orbit as long as it's spinning around the star, it'll even negate its own weight and reduce stress on the structure if it's spinning at the right speed.
http://physics.stackexchange.com/questions/41254/why-is-larry-nivens-ringworld-unstable
http://www.popularmechanics.com/space/deep-space/a11183/could-we-build-a-ringworld-17166651/
Larry Niven actually addressed the issue of drift in The Ringworld Engineers after some of the smarter fans realised the problem