Please don't subject any cats to rats! Rats can kill a cat, especially if the cats can't escape! Think of the weight of a rat compared to a normal cat - about half or more! Now to the rats. You don't say what kind of rats. There are 'Roof Rats' that live high up in sheds, barns, etc. and there are Norway rats that live down on the ground and dig burrows.
Remember, like a mouse, rats can get through any hole, if they can get their heads thru, so look for where they are getting in at and put 'strong Hardware cloth' over those holes. Since they can dig holes (I've seen plenty in horse's stalls), you'll have to reinforce the shed floor with metal of some type.
Those rats found a smorgasbord in rabbit food (actually, they'll eat most anything) and they aren't giving up easily. You've got to enclose your rabbits with metal, just like if you had a chicken coop to keep varmints out. Put the rabbits food in secure metal cans, too. Also, rats carry diseases and/or rabies. (Information from hubby, who is an exterminator 30+ years)
For God's sake "never" use poison products near any animal. The Rats may be eating the poison you have left for them but if they have access to the Rabbits pen and leave their "droppings" this can be a huge problem. Have you considered removing "all" poison and replacing with two Cats? Good luck.
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