A simple pun somehow turned into a worldwide celebration of all things Star Wars. It’s futile to try to pinpoint who first made the joke, but Zaron Burnett at Mel Magazine tries to pin it down.

With Burnett’s investigation, it seems to me the real culprit is Randy Thom.

It was further popularized by Randy Thom, the director of sound design at George Lucas’ Skywalker Sound. On May 4, 1982, he was working on Return of the Jedi when his brain kicked over the pun, and he just started telling his co-workers, May the Fourth be with you.” The bit was good for morale and well-received, so he brought it back year after year after year, spreading the pun around the company. 

I’m rather partial to Revenge of the Sixth” to indicate May 6.