Saddly if there is 1 rat there will (or can) be many more. A cat would be a good idea, but then that would make it an outdoor car & that solves nothing, as cats shouldn't be outdoors, as they kill song birds, dig up gardens, get into fights, get hit by cars & people kill them... I assumed it being an outside cat, because why would you have a cat in a bird cage? hehe

Just be careful if you go the cat route... but traps might be better.. just remember if your going to move the rat, that you don't make it someone eles problem, as thats kinda rude :P

Hope you can find a way to solve the issue.