Using poison to kill the rats would be the best solution in actually killing of the rats and especially if the rats are large rats.
But if you don't want to put out rat poison you can buy glue traps, snap traps and even traps that will electrocute the rats and kill them.
If you set the glue traps out where the rats are they'll get stuck to the trap and not be able to get back off and the snap traps will close down on the rat and snap it's neck and kill it.