In order to get Regigigas on your team, you'll need to fulfill several requirements. First, you need to enter the Hall of Fame and have your Pokédex upgraded to the National Pokédex. You'll then have to catch Regirock, Regice, and Registeel, and have them in your party.
A girl in one of the homes in Pacifidlog Town holds some hints to fulfilling the other conditions you need to meet. However, the hints that she gives differ from player to player. There are four different hints altogether. Swap stories with your friends to collect all the hints!