My method for combatting mice (haven't seen any rats) is to take all the chicken food out of run at night. What I give the chickens to compost in their run either isn't of interest to mice (leaves, bark, grass, weeds), or gets totally eaten (squash guts, etc.). I take out "chickie snack" in the early afternoon, and by lock up, there isn't anything left.
Anything icky/moldy/rotten/rodent attractive gets put into the compost bin. And covered in chicken poop. Some gets dug up, but hey, if something wants to eat poop-covered slimy banana peels....
I'm going to pick up some grass seed in preparation for moving the coop down by the garden in a couple of months. I'll reseed the area that was the run last summer, and maybe they'll have some tender little grass to eat when they get down there. When they move, I can reseed the area where they are now, for when they move back next fall.
The dirt in the run right now is some fine looking dirt!