If you have the right ring, I can't see why not. It's a stick with a motor, should be just fine.
I may be wrong and corrections will be following any second!
If you are asking about the Weber 7519 rotisserie kit for the Genesis, then no, it will not work. The spit for the Genesis is square and machined round in two spots so that it can spin in the Genesis' firebox grooves. Those rounded areas are too far apart for the Weber 2290 kettle rotisserie ring.