we've got barn cats, they've got a job just like the rest of our animals, and they do it well. and they run loose because, well you know, that's where the mice and the moles are. we see bits of what they eat, mice, rats, moles mostly. I've seen bird feathers once this year, and it was a mocking bird so likely it was harrasing the cat when it got nabbed. they don't bother our chickens who free range during the day. or the ducks or geese or the turkeys or the guineas. in fact when I put out food scraps, the cats and the chickens, turkeys, guineas all get in there together to eat them. we don't free range chicks or poults, just to prevent problems.
cats don't have to be a problem, and they don't all kill birds on the endangered species list. our barn cats are outside on purpose, they've got work to do.
the alternative to barn cats is traps or poison, both of which work less well and are far less discriminating in what they kill than our cats.
the house here was overrun with rodents, rodent stink, and the smell of rotting rodents as the landlord had tried to handle the problem with poison. it took 25 hours of work to get the kitchen clean of rodent trails and poop and the rodent smell to a tollerable level. and then we still had to wait for the rotting rodent smell to discipate, that took another 2 months. I thought we were going to have to pull the cabinets to get the stink out.
so our barn cats and house cats hunt and we keep the chicks and poults penned. much better solution.
to the OP, sorry you've got a cat harassing your birds. lots of solutions to choose from here. just know the chickens might not be the only thing they're interested in hunting, perhaps it's a problem of changing their focus.
FWIW, some of our barn cats are domesticated, some are fully feral, all eat with the chickens and don't bother them.