I’ve caught a few rats that way, but, rats seem to wise up to most ANY kind of trap pretty quickly. I’ve had more luck, when I’ve had time (rare, these days) to plink ‘em with a scoped pellet rifle, as they don’t seem to learn to stay away from the chicken feeder for long. Also, I’ve observed our (newly adult) Buckeye chickens chasing mice and small rats. I’ve never seen one catch such, but, we seem to have less rodents now...
(Our cat helps, but she catches more small moles, voles, and small reptiles and amphibians than mice or small rats.)
The usual rat MO seems to be to dash out for a piece of food, go stash it, and come back for more. Good shooting. As a kid, I remember my grandfather’s hens chasing mice, and I’m pretty sure they’d have eaten them if they caught them. So I was surprised when I went to a friend’s house, some years back, and noticed motion under a bush. I looked, and there were several mice eating chicken food. This guy threw it around pretty good, which kind of annoyed me because I had a few roosters farmed out to him while their feathers developed, and I was paying more to feed them than my home flock. Obviously the chickens were too well fed to care, but it still struck me that all of these mice were out during the day, so I asked about it. He said it was because they didn’t dare come out at night because of the rats. I asked how bad could they be, and said I should stick around for dinner. After dark, we walked out to the shed complex, and he turned on a light. Oh. My. God. Walls, ceiling beams, shelves, and the floor turned into streams of rats running for their holes. And this guy was a shooter. Must not have had an air rifle. He could have set up a dim light and sniped rats all night, probably for weeks.