In fiction cats are often chosen as the optimal zero/micro gravity pet. Clearly there is some rational for this, all existing answers at How do astronauts turn in space? include cats in them.
While most litter boxes on Earth use sand or some pseudo dirt substance, it seems unlikely this would be a good solution without significant gravity. It is possible to teach a cat to use toilet so a space cat using a toilet is an option. Though it looks like current space toilets use different facilities for liquids and solids so not the best option for a cat. How would a zero gravity cat toilet/litter box work?
While there have been a lot of animals in space they have all been confined, this question assumes a cat with free range of the environment like it's human companions. This question is about the mechanical/physical solution not the training issues which would be best addressed at Pets.SE