No. George Clooney did not appear in the 1993 film "Tombstone". The role for the Cochise County Sheriff was played by actor Jon Tenney.
See "Tombstone" full cast and crew on IMDb.com.
Jon Tenney's connection to Clooney is through his ex-wife's (Teri Hatcher) alleged romance with George - which she admitted not true. “We went to one dinner back in December, and that was it. No kissing," Teri said.
See George Clooney full list of movies and TV shows in theaters, in production and upcoming films at TVGuide.com.