do check the shelters.
They often have cats they deem too wild to become pets. They need a home, too. Some run 'barn cat specials' now and then.
You do have to provide the cats with a location to put them up for a few weeks before you can let them out! Preferably with a window.
And of course...
what chickens do you have?
I am thinking that a full grown chicken is a bit too big for a cat to take on.
Having said that, my one cat is a lump at #14. And she likes to hunt birds.