It is easy to get rid of rats.  Stop feeding them chicken feed, they go elsewhere or starve. 
 Normal foraging for natural food keeps their numbers way down and rats are not a problem until a human sets up a buffet for them.   It is that simple. 
How you choose to pay to do this is another matter. 
Pay for poison forever more.  Take the risks that entails.
Spend the money once on a treadle feeder and the time to clean up around a coop and yard.  
Pay for traps and your time trapping and the cost of the traps, assuming they work after you catch a few of the more stupid rats.   Buy new traps, wash, rinse, repeat.
Or you pay for a rat proof coop assuming they don't free range.
Or you continue to pay far more with buying more expensive chicken feed and live with the non stop influx of pests and disease and the increased numbers of predators that love rats and love chickens too.