"Rudy" is the adjective you are looking for (it could be used to describe a red/ginger coat of an animal or a person's hair: "Ruda dziewczynka ma rudego kota" = "A ginger girl has a ginger cat"). Using "pomarańczowy kot" would sound rather 'clumsy' if you were describing a real animal.
Ginger is a very common adjective to describe a cat in English. Should we by ngfio's comment understand that "pomarańczowy kot" does not describe such a cat but can only refer to a (probably not real) cat that has actually been painted orange?
of course, but it is better to use word "rudy" if you are speaking about cat (also about some other animal or about a color of person's hair). "Pomarańczowy" is better to use, saying about for example a wall, a furniture, a car etc.