No one here can answer that.
This is completely up to you as a parent, prudentially. It depends greatly on where you live, the maturity of your individual child, the logistics involved, and other parents and their practices in your area.
When I was a kid, we were dropped off at the movie theater by ourselves when we were in 3rd grade, went to the movie, then got picked up afterwards. I don’t think that would be popular parenting now.
In my small town where I live, kids could certainly walk or bike to the movies at age 12+ by themselves without danger. In a large city, maybe/maybe not depending on the situation.
You need to examine the situation where you are and make your own decision. Also impacting that would be if other parents are going to let their children go with your child by themselves.