A rooster is, of course, a male chicken, and only hens, or female chickens, lay eggs.
But every now and then, a disease may cause a rooster to change its gender and become a hen, or vice-versa. Some of these roosters-turned-hens have actually laid eggs.
But this still does not mean that a rooster can lay an egg; it’s still true that only a female chicken can lay an egg. The most we can say about the rooster’s egg-laying ability is that some roosters that turn into hens can lay eggs.
Sometimes, small, misshapen eggs found in a hen house are called “rooster’s eggs.” But these are simply hen eggs that failed to develop properly.