Short answer: technically feasible, but politically impossible. No one would let a nuclear-tipped anything within a hundred miles of the ISS, or into any permanent orbit in space at all.

Best bet would be some device that could place a powerful thrust system (there are many options here) on the surface of the asteroid and deflecting it by applying thrust constantly over large periods of time. This is technically more difficult than placing a bomb on the surface, but would be much more controllable. It would be politically more palatable too, until someone realizes that such a system could also be used to direct a rock AT the Earth.

The latter is not really an issue, since it would be very difficult to do something like that without the perpetrator being obvious, and rendering themselves susceptible to more conventional military attack long before the rock shows up. The perpretrator would almost certainly have to be an advanced nation, which fortunately rules out the average "blow-up-the-world" looney terrorist.