Pokémon the Series: The Beginning
Hiker used the Rhyhorn against Ash's Bulbasaur. Bulbasaur attempted to use Leech Seed, but got a nasty welt after getting hit by a Take Down. To end the battle, Bulbasaur used Razor Leaf and defeated Rhyhorn.
Like its trainer, Rhyhorn appeared in the opening scene of Adventures in the Orange Islands.