Go to the local hardware store, and you can buy rat and mouse traps that are "live" traps (used to humanely catch mice and rats) and you can bait it with delicious things and then hide it underneath some of the furniture. I typically use peanut butter for escaped rodent baiting since they can't grab it and run away with it.
We are as gods to the beasts of the fields. We order the time o' their birth and the time o' their death. Between times, we ha' a duty. - Terry Pratchett.
"Men have forgotten this truth", said the fox, "But you must not forget it. You become responsible, forever, for what you have tamed. - Antoine de Saint-Exupéry