Giovanni owned a Rhyhorn in Red and Green, Yellow and FireRed and LeafGreen games. It debuted in Pokémon Red and Green, being at Lv. 24 and knowing Horn Attack. In later encounters, it is Lv. 37 and knows Tail Whip and Stomp and in the Gym Battle Lv. 45 and knows Fury Attack as well.
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In the Pokémon Adventures, Rhyhorn debuted in Red's Gym Battle against Giovanni.
Later, it saved Yellow from Lance's attacks and soon after, Giovanni appeared with her.