If the tube feeders don't keep the mice and rats out for you, you can place the good-old-fashioned mouse traps against the walls with the trigger closest to the wall in an area that other animals such as cats, dogs and chickens cannot get to it. Check the traps every morning. The dead catch is perfectly fine to feed to your chickens and will encourage them to become your rat catchers quickly.
I once moved into a house that a significant mouse population at the property, for about a week or so. I used this method to teach my chickens to hunt and as mentioned... the significant population only lasted a week or so...
I'd like to point out that this method quickly dispatches the mice, it's over very quickly for them so they don't suffer. They're not fed poison, and therefore won't poison any animal that eats them.