Feeding the birds can be a cause of rats in your garden.
If you want to feed the birds do not throw food out for them instead use a bird feeder that does not allow crumbs to fall to the ground. If you have a rat problem remove the feeder completely. If you have animals or pets then make sure that rats cannot gain access to their feed. Keep all waste, especially food waste in a sealed bin. Rats will have regular routes to food sources and can often be found nesting under sheds, outbuildings, decking and compost heaps. Ensure that your house has no holes or gaps which a rat could enter as they can cause damage in the home and also carry disease.
You can remove rat infestations however it must be done humanely. Traps are not usually very effective as rats breed very quickly. Rats can be poisoned with rodenticides however there are health and safety issues with using poison bait and you must ensure that you read the label carefully and do not kill other animals.
There are local and national companies that can also provide a similar service, try searching a local telephone book or the Internet for pest control.