Yes, cooked. Plain cooked egg is a safe protein treat for cats. Raw eggs can carry Salmonella.

Can Cats Eat Eggs? Yes, in small amounts

How to give eggs safely

Scrambled or boiled, fully cooked, plain.
No butter, salt or seasoning.
A small amount as an occasional treat.

If your cat ate too much

If your cat ate raw egg, watch for vomiting or diarrhoea and wash bowls and your hands.

Sources

ASPCA — People Foods to Avoid Feeding Your Pets
FDA — Get the Facts about Salmonella

General information checked against published veterinary sources. Every cat is different — ask your vet before changing its diet, and call them if it seems unwell.