I think you'd do better with a small terrier or a couple of ferrets. Cat's aren't reliable ratters.Open the door and throw in a big tom cat. Award the winner with a treat
But seriously they are filthy animals that do carry disease. Maybe call pest control to get rid of it and check for others(a nest).
Rats are as clean as any other animal, and any animal can harbor disease. I daresay Riders' risk of disease from human contact outweighs the risk from a few rats, squirrels or
If the local rats were carrying some disease, it would probably already have become news.