My wife breeds and shows maine **** cats but the only one allowed out (the others have a large run) and is now too old to care. In her younger years her record was 10 field voles in a day, rats, pigeons with a live squirrel and a water rail let loose in the house. In earlier days we had a moggie that we found tucking into a rat under our bed FFS.
We have 2 maine *****. Trouble is they're so laid back, they can't be bothered with sitting there for hours hunting rats. They will get the occasional one though. (The feral cat that turned up on the farm one day was far more successful before he died )
Our working line labradors though - well - those rats had better watch out. (It's only the electric fence that we have protecting teh chickens from the fox that saves he rats from the dogs....)
Air rifle gets a few - but not many tbh - rats are clever, fast, and can work out quickly where you shoot from!
Glue traps are very effective, but need a lot of care - and you need to kill the b***gers your - self - and the screaming whilst they're stuck is HORRIBLE.
Jack Russell is the answer - but if you don't have access then poison probably - and coated corn grains in my experience.