YMMV depending on your cat, and it’s impossible to tell what it’s going to do before getting one. My brother’s apartment is mouse-infested despite having a cat. It’s actually worse having him around. He’ll catch them, play with them for awhile, maiming them in the process, and then carry them into my brother’s room and leave them on his pillow as a little token of love. Then it’s up to my brother to dispose of the mutilated, but still alive, mouse, and deal with the bedding. He didn’t get a cat specifically to deter mice though, just wanted one.

When I had them, I used to just catch them in an electric trap and make my husband throw away the corpses—much easier and no one’s pillow was defaced in the process.