Lots of good ideas here but stopping feeding the rats doesn't work. They can find food anywhere and they won't leave a good shelter, especially with winter coming. We had rats living in our barn years before we ever had chickens, and there was no animal food out there for them to eat back...
Please don't use poison. I hate rats too and we have a bad problem with them here, we've had chickens for 20 years and never had a rat problem like this year. I've knocked them down with Rat X ( I dust the pellets with cocoa powder or powdered sugar), traps, and cocoa powder or powdered sugar...