Rhyhorn was first seen when Red was on the ground after the Viridian City Gym collapsed; he and Giovanni were having their battle.
Two years later, Blue recalled the events that transpired with Red in a flashback of Red's battle against Giovanni, which included his Rhyhorn.
After disappearing with its trainer for two years, it appeared with its trainer to help Yellow. Giovanni had Rhyhorn use Horn Attack to pierce the bubbles caused by Lance's Dragonairs an his his Gyarados and Stomp, for the dust from the ground to show the blubbles.
The Association recalled Giovanni and his Rhyhorn, as the two went missing after the battle on Cerise Island, leaving Viridian City's Gym empty and without a leader.