If you know someone with a Jack Russell or other rat-type terrier, that would frankly be the simplest solution
I have never caught a rat in a snap trap and I'm not sure I've ever *known* anyone who has, either, although I'm sure it happens occasionally. Live traps either.
If you are not 100% averse to poison, one option is to set out a dab of peanutbutter where the rat will find it, for a night or two, then on the next night combine the peanutbutter with as much dry plaster-of-paris powder as it will hold to make a dough that you can roll into a marble-sized ball. Leave a couple of them out, and unless it is a rat from very wise-to-the-ways-of-the-world lines, it'll probably take care of your problem. Having plaster heating and hardening in your tummy is doubtless not a terribly pleasant way to die, but sometimes you just cannot let rats take over the world, you know?
I've had rats *inside* my chicken bldg a couple times, and caught them by flushing them out from their hiding places and then standing on them and severing the spinal cord with a knife, but that is unlikely to be workable outdoors.
Really, a rat terrier would be happy to take care of it for you.
Good luck, have 'fun',
Pat