Universal Studios Hollywood. They started tours of their studio lot in 1915, charging people five cents, then multiple attractions popped up in 1964.
If you call walk through of sets, back lots, and riding a tram an attraction. That didn't come until several years later. Universal may like to state the California "theme" park started in 1964, but not really. Not when you are comparing yourself to theme parks like Knottsberry and Disneyland. I would call what started in 1964 more of an enhanced back lot tour, not a theme park. Even in 1983 (last time I visited) it was still very much a back lot tour with a guide since it was and still is a working studio (don't want guests to mistakenly wander onto working lots) - the only thing I would call a ride was Jaws.