I agree with what has been said. Rat poison, whether ingested directly by your cat, or from a rat that has ingested it, will kill your cat.
Large wild rat populations are commonly infected with Leptospirosis. It cannot infect cats, but it can infect dogs and then be passed to humans, via urine.
Also, what area are you from? If you are outside the UK, I hope your cat is vaccinated against rabies, as bats are common carriers.