The quick and inexpensive: If there is room in the coop get a couple of the Big Victor Snap Rat Traps. Tie some raw bacon to the treadle and rub a gob of peanut butter under the treadle (rat either pulls at bacon or jams snout under the treadle). Place traps under heavy duty cardboard (or whatever you have that is just big enough to allow the kill bar to move freely) box, cut rat sized holes in the edges of the sides where box will touch ground, flip boxes over traps and place bricks on top so birds can't knock them around. Rats will walk in and that is that. Also, cut a small hole in the bottom of the box just large enough to look down into to so as to check for whacked rattus without having to move the box.
Rats are disease vectors, and there have been members who've posted that the rats moved in on the birds and gnawed a bit...
Remove any chicken feed from coop at night so as to encourage rats to seek out the entrees on the Victors.