What's the best way...

What's the best way to kill a wild rat? I'd really rather not do it at all, but my sister's cat got a hold of a wild one today and it's very injured. Internally, nothing on the surface. It can't even stand. I have it in a cage outside (old rat cage that I wasn't ever going to use again anyways). It's in the same 'air space' as Betty, since my window is open, but there are rats outside all the time anyways, so I don't think anything bad will happen. I would take it into a vet or call animal control, but it's too late to go out. I doubt it will live until morning, so I suppose I could just leave it to die that way, but any suggestions to make it's passing easier are welcome.