Any animal can be your spirit animal. If you feel like a cat is, chances are it might be.
One good way to find out is to keep a dream journal. Meditate and focus on the intention of discovering your spirit animal before bed. When you wake, immediately write down all that you recall. If an animal appeared in your dream, what did it do? What did you feel?
Animals you feel a strong connection to may be your spirit animals. Spend some time around, or thinking about/studying different animals and see how you feel. Someone once suggested to me to make a list of traits about myself, then compare them with traits of an animal you feel attached to. You could try that.
Best of luck. :)