Depends on a particular cat's preferences, but some I knew were pretty lethal rodent (and bird) removal agents.

In seaside cottage we had I used to use a trap (essentially a wire cage with funnel-like opening on the top) baited with cheese and/or bacon. It worked (not spectacularly well), and I resisted temptation to release the critters in my neighbor's yard, driving them instead to a forest a few kilometers away.