While pennies minted in the US after 1982 are largely copper-plated zinc (only 2.5% copper) and are unlikely to provide copper in high enough concentrations to harm birds, birds can still develop copper toxicosis through environmental sources, especially birds of prey that ingest contaminated prey.
Additionally, pennies are an unnecessary item in bird baths, and even small amounts of metal contamination can alter bacterial processes in bird feathers, potentially contributing to bacterial-induced feather damage and disease. To err on the side of caution, it is best to avoid using copper pennies in a bird bath.