This might seem like an odd question to some. The short answer is that before 1985, no and she had to use a invisible plane to get around. After 1986, her character, among other DC characters, went through a transformational change to help establish continuity and ground rules. At this point she was given the ability to fly and began to be arguably comparable to Superman and his abilities. But how do we know Wonder Woman can fly? In the 2017 movie, for example, it appears that she cannot fly at all. So we need to dig a little deeper for the explanation.
In 1985, the DC universe went through a transformation with the story arc Crisis on Infinite Earths. It was a terrible story and hard to follow, but it had to be done. With all of the different dimensions and stuff with different variations, things had to be simplified. And one of those simplifications was to give her the ability to fly rather than have to rely on an airplane. You see, before the transformation in the story arc Wonder Woman would get around in an invisible plane with peculiar properties. But since things had changed and she was given the gift of flight, the invisible plane was something that began to be neglected.
But how can Wonder Woman fly in the first place? The answer is in the first issue of Wonder Woman from 1987 (Affiliate Link). The Greek deities together created her out of clay and each one gave her a special attribute. Hermes, in particular, gave gave her the gift of flight. We can see her fly for the first time (since gaining her new abilities) in Wonder Woman issue 2. Hermes himself is present during the event.
Now that you know the history, what are your thoughts on Wonder Woman being able to fly? Would you rather she stick with her traditional invisible plane? Or does flying make her more comparable to Superman? Leave a comment.