If it's infested, you're going to have a lot of work ahead of you. You need to clean up VERY thoroughly. Keep all food tightly secured in metal containers, clean the coop and yard, clean up any hay or straw piles/bales, underbrush, trash, or woodpiles that the mice could be nesting in. Mice don't stray far from their nests, and nest when conditions for food, nesting material, and hiding spaces are right. Fix ALL holes you find in the coop. Mice can squeeze through holes the size of a DIME.
Eliminate the resources, they will have nowhere to keep making baby mice.
As for the current population, start setting traps. I recommend bucket traps and snap traps. Avoid poisons because chickens eat mice quite happily and they will eat an easy meal of a dying, poisoned mouse.
For a bucket trap, get a large bucket, fill it up about halfway with water and spread sunflower seeds on the top of the water to float. The mice will jump in and drown.