My chickens tend to get rid of mice on their own. It's a great game for them when one hen finds a mouse and plays keep away with the others chasing her for their chance to eat a mousy. That's one of the reasons I LOVE ads that say producers raise their chickens as vegetarians. Chickens have no ethical problem with meat eating.
I store feed in metal garbage cans to keep mice out and try to never leave feed in the coops overnight. If you don't want to kill the invaders, you can use one of the small no-kill traps and relocate the mice. Kness Mfg. in Albia, IA, makes a metal trap that doesn't need bait. The smaller Ketch-Alls rarely kill the mouse. Sometimes, because of the way they are manufactured, the larger Ketch-All will assassinate a mouse that gets hurt in the mechanism, although they are not supposed to.
Rats are much harder to deal with. Much.