My cat partially ate a rat that she caught outside, should I get her seen by a vet?

Rats do carry many things - the most common ones are parasites (worms), fleas and ticks, but your cat is already exposed to those since she is allowed outdoors. The biggest thing you have to worry about is poisoning. Many people put out baits to poison rodents. The problem is that when another animal, or bird of prey, eats the poisoned mouse or rat they too become poisoned, and die without getting treatment. I'd be scooping up the carcass, and take it to the vet to determined if it was poisoned or not, so that if it was your cat could get the emergency treatment she would need. Of course you are going to have to pay for the testing on the rat - but that is the price you pay for having a cat that is allowed outside.

It does happen and if it will set your mind at rest, do get her checked. But I will add that I once lived in a tropical climate with a whole bunch of animals who hunted rodents and they were always OK. But a potential serious problem is that rats have often eaten warfarin which thins their blood so that they bleed out and die. It's a well recognised pest control method.
So that won't do your cat any good either. Plus it makes worming absolutely essential and definitely a flea treatment too. It's a difficult thing because cats will hunt and they will catch rats and mice. She's probably done so before and you haven't seen it, so always worm and de-flea regularly, and a check up every six months at the vet, or other visits if anything else seems wrong with your cat.

She'll be fine

Not because of the rat specifically, but if she is catching rodents then she should be getting worm medicine several times a year. Stuff from the vet, not an over-the counter one. Catching and eating small animals is what cats do and their bodies do it very well. That is, in fact, the historical reason why they have been associated with people for some thousands of years. They help keep rodents under control.