A bird pecking on your car mirrors is not only harmful to the mirrors, it can hurt the bird, too. This seemingly odd behaviour is a result of the birds thinking they are fighting other birds, usually for territorial mating rights. Mirror pecking is often the worst during the mating season and is usually seen in more aggressive birds, such as the cardinal. There are several options available for stopping them from pecking away your mirrors.
Wrap the mirror with a plastic or paper bag, making sure to tie it with string so it doesn't blow away. This will block the birds from seeing their reflection and may scare them away.
Cover the mirrors with a dark sock. The socks won't scratch the mirrors, and they will stretch to fit over the mirror in most cases, making using string unnecessary. They are also easy to remove.
Cut cardboard pieces in the shape of the mirrors and place them snugly over the mirrors. If they don't stay in place, use small pieces of tape to attach them to the mirror casing.
Keep the mirrors covered for at least a few days. Birds are territorial, even more so during their mating season, and will often have a nest nearby, so they may come back at some point.
Don't drive with your mirrors covered, as doing so may be violate traffic laws and create an unsafe situation.