Odds are no.. but you never know. Anything is possible.
I assume you mean "Have the events in Star Wars actually transpired" rather than "Does the movie itself exist?" To answer both, yes, the first movie came out in 1978, therefore, it does exist. As for the story being authentic, the odds of such a thing being true are very near 0, then again, it would have already taken place, a long time ago, in a galaxy far, far away.