Yes, animals can be possessed by evil spirits, as is attested to by the Bible (e.g., Matt. 8:30-32
). But I recommend that you take your cat to the veterinarian to rule out any medical or behavioral problems before doing anything else. (Ruling out medical and psychological problems is what must be done before human exorcisms, anyway). Only if there is no medical or behavioral explanation for your cat's problems, then consult with a priest to see what can be done.