Can we disrupt the orbit of an asteroid to follow earth's geostationary orbit?

We could, for a very small asteroid.  In fact, there is a design for a mission that would go out and capture a small asteroid and bring it back and put it in lunar orbit so we could study it.

However, putting an asteroid, no matter how small, in geostationary or geosynchronous orbit would be a terrible, terrible idea.  Those orbits are needed for critical communications satellites.  Putting a big rock there that we would later not be able to control as its orbit was perturbed or as it shed debris could bring upon Gravity type scenarios.