A cat might not be able to take on a large rat. A rat terrier would be a better choice.
Small dogs like rat terriers can do em in. The dogs do sometimes have the unfortunate habit of chewing and clawing at furniture, doors and walls to get at their prey. Cats are the best because they have the instincts and patience that is needed to be still and wait for the right time.
We have lived and again live at the edges of wooded areas in a city residential area. Rats and mice as well as racoons have a tendency to come in when winter approaches. One good cat can keep the vermin at bay. Haven't had a problem in years.