Yes having backyard chickens can attract rats and other rodents to your yard.
The rats and other rodents are attracted to the feed and water you put out for the chickens and not the chickens themselves.
If you do have chickens it's best to put out some rat traps near the chicken coop to trap any rats that may be coming around your chickens.
Also using hanging feeders or feeders for chicken feed that keep the chicken feed off the ground is also a good option.
It helps prevent rats from knowing about the feed and makes it a bit harder for the rats to get to the chicken feed.