It depends on the circumstances such as how much you have talked on the phone or been in contact via email and so forth. Is it a movie you've both been "dying to see" and is the movie the (only activity) you have planned.
Most people automatically say going to a movie on a first date is a bad idea because you're NOT talking to one another. However I generally would not ask anyone out without having a few lengthy conversations to begin with. I'd already have a sense of them.
I don't approach every date with the idea that she might be "the one" but I do attempt to pick an activity that I believe we'd (both enjoy) even if there was no chemistry between us. Movies, plays, concerts, or festivals can be fun. Having a good time together is the goal.
Nevertheless simply going to a movie and (parting immediately) afterwards is not much of a date! There should be some time that you enjoy each other's company. An early movie followed by a late lunch or an early dinner on a Saturday/Sunday or vice versa can be a nice outing. Maybe the (first date) in this scenario should be lunch first followed by the movie. The goal of a first date is to determine if their is any "chemistry" between you that would warrant going out again. Keep things light/relaxed and have fun!