This is not a really good idea for two reasons..
First:
Cats are not "nature's little pest control". They kill many other things, like birds, snakes, voles, lizards, frogs ...These are native animals that are essential to a good ecosystem. Most of these things are easier to kill than rats and mice, so THESE are what your cat will really be preying upon. Not what you intended...
Cats are non-native predators. Many native animals don't have very good defenses against this type of predator. They are an ecological problem all over the globe, but a very large one in the United States.
Second:
... if you really care your cat, you'll keep him as an indoor kitty only. There are many, many, MANY bad things outdoors that can kill and injure cats. There are cars, cruel children, cruel adults, diseases like feline leukemia, parasites (both external and internal), and other cats which will try and kill or maim your cat.
Talk to most vets or people who work in vet offices. Ask them how many injured cats they see. Ask if they are indoor or outdoor...
Ask what the lifespan is of an
outdoor cat compared to an
indoor cat.
Ask yourself why you wanted a cat? Is it because you want a pet?, ..or did you hope for a pest control device?
If you want a cat, you should get one, they are awesome pets ...I have one on my lap right now.
However, if you want something to kill pest animals, get some traps. They are much more humane ...both for the rat, and for the cat.
Bob