Scrub your grill rack with a steel brush to remove any stuck-on foods. Rats will find even the smallest piece of leftover food.
Clean the barbecue as soon as it has completely cooled. Even if there are no remaining food chunks, the rats will still smell the food. Cleaning will eliminate food odors.
Plug up all possible entry points that would allow a rat to get into your barbecue grill. Use wads of aluminum foil or balls of steel wool to do this.
Cover your barbecue with a grill cover for extra protection.
Store your barbecue grill away from trash cans (which should be covered with secure lids) and piles of wood that might attract rats.
Mow your lawn on a regular basis to keep the grass on your property low. This is important since most grills are kept outdoors. Tall grass attracts rats, as it provides them with a place to hide.