If he's a registered Angus bull, the calves should be polled. But they'll carry the horn gene, so if you keep heifers and breed them back to a bull carrying the horn gene, those calves might have horns.
The polled gene is dominant so if he is a purebred Black Angus there shouldn't be any horns. Just make sure you breed them to another polled animal to ensure that they stay polled because they still carry the horn gene.