I found a mouse in my kitchen years ago at my old house, they tend to come into warm kitchens when it gets really cold outside. Tried leaving my cat in the kitchen, she lasted 5 minutes before scratching on the door and crying to come back into the lounge so that wasn't really a successful measure.
You've got to block up any holes a rodent can get through - and mice can get through surprisingly tiny holes with surprising ease. We ended up with mice living in the ceiling space, scratching around at all hours of the night, quite disconcerting if you're up late watching a creepy film.
Humane mousetraps are available, if you've really got to trap the rat then I'd recommend those. Not only for animal respect reasons, if you've ever had to clean up a squished rat in your house then you'll appreciate being able to dispose of the rat miles from your home.