Cats can safely eat eggs. Eggs usually have no harmful effects for cats and are a great source of protein for the majority of house cats.
Cats are obligate carnivores, meaning they need meat and animal protein in their diet. Eggs are a great way to supplement traditional kibble. Both cooked and raw eggs are good options, but to decrease the likelihood of salmonella, cook the eggs before feeding them to any pet. The shells are a good source of calcium, so consider crushing a small portion and adding them to the cat's food bowl. Some cats are allergic to eggs, however, so watch for any negative reactions.