My two cents: if you treat it as a proper responsibility and as essentially a furry child, you have no moral or ethical qualms. If you can satisfy its needs and help it lead a pleasant life free, that's enough.

On a related note, I had a professor in college who was a Buddhist and considered his living situation as involving a "cat who lived with me" and not "his cat" per se. I think that's a much healthier way to look at it. It preserves the cat's agency and rejects possession of another living being.