Cats can work but don't let hem roam the neighborhood. They kill Billions, yes, with a "B" of native birds every year in the US.
Don't use poison. Poisons make their way through the food chain. You kill a rat with poison, it's a slow death, does and dies somewhere else, predator eats said rat, predator dies, vultures go to eat predator, vultures die. I recently picked up a screech owl in the road in front of my house that basically looked really drunk. Was actually dying from pesticides.
Try traps. The guy that runs Mousetrap Monday's youtube channel has hundreds of videos about all different kinds of traps.