I use both bait and fen traps for rats. Bait is the most effective means of control for me, but as Daniel1005 points out, it can be lethal for other animals. I use wax block bait as opposed to laced grain, as it's less appealing to other wildlife, and I supply it in purpose built and home made bait-boxes that prevent pets access to it. Most poisons available are multi feed killers, which means the rat has to dine on it several times before it kills them. At first all you will find is your bait vanishing and very little else, but after several days you will start picking up dead bodies or finding dopey rats near death. These dopey rats are usually easy to kill with a spade or stout stick, then incinerate the cadavers. Not particularly pleasant I know, but it is the most effective control.
If your local council provides a vermin control service, either free or at cost, they will bait with one feed poisons that will kill the rat after one helping.
Fen traps are also useful, but must be set so other animals cannot get to them. Look for where the rats run, and set the traps in their path. Rats usually like to travel close to walls or other protective cover, so you can often cover the traps, creating a tunnel, by leaning a board or such like against the wall. That or create tunnels over more open runs by using bricks, board or whatever is to hand. not all trapped rats are killed outright, sometimes they are caught by a leg or their hind quarters, and will need to be dispatched as quickly as possible, so check traps regularly. Live traps can be useful, but then you have the dilemma of how to dispose of the incarcerated creature! Old timers used to submerge the entire cage in troughs of water or water butts and drown the contents! but with todays more precious approach to vermin control, other means of disposal will probably be favoured! release of the captive is NOT an option!!!
Another method of control that works well, particularly in more open situations, is smoking or flooding the burrow systems, thereby flushing the rats into the jaws of waiting Terriers! I have two JRT's that particularly enjoy this approach! A word to your local Gamekeeper, Vermin control man or Working Terrier enthusiast will probably see an eager team turn up keen for the sport, and at the same time rid you of your problem! just remember to keep your birds shut in! Not ALL Terriers are trustworthy with chickens!