He caught him in the 1980 episode "Soup or Sonic." The episode was directed by Chuck Jones, which means it counts as an official Road Runner cartoon. The episode was part of a Bugs Bunny special "Bugs Bunny’s Busting Out All Over"
THE SCENE: It started like all of the other chases, with the Coyote in hot pursuit of Road Runner. Wile E and Road Runner speed through a series of pipes that shrinks them down in size. The Coyote figures out what’s wrong and they go back through the pipes.
But only this time Road Runner increases in size, while Coyote is still small. Wile E. Coyote does finally catches the Road Runner, watch and find out how: