First, you need to make sure that it is in fact a rat/rodent burrow you are observing around your home.
Rats create underground pathways or burrows from their nest to food sources and to escape predators. These burrows are often located under bushes or other types of dense vegetation. Rat burrows usually contain a main entrance and 1 or 2 exit holes away from the main entrance. Check along walls and grass for runways. Rats run along the same areas over and over leaving worn down paths in grass and dark greasy track marks along foundation walls. Fecal droppings (3/4 to 1" long) along their runways or in areas where they have been feeding is another sign of a rat infestation.
Once you have determined the extent of your rodent/rat problem, there are several nonchemical control methods you should follow first.
Trapping and rat poisons (rodenticides) are options. However, rodenticides should be administered by a pest management professional, as they can be lethal to pets and non-target animals.
Find more information about pests in eXtensions Pest Management In and Around Structures Resource Area.