Very interesting question. Depending on the size of the rat, there really should not be a problem unless the rat tries to enter the nest and eat the eggs. The major issue is to feed the swans in the water approximately 3 feet from the bank. If you leave food onshore, it will attract rats, ants and other pests.
Now, having said all of this, if the rat is not a rat, but rather a mink or such a larger animal, it can attack and kill the cygnets (baby swans). If the rat were to swim further into the water, the swans would probably try to drown it. We hope this info is of benefit. The Regal Swan