Hayabusa-chan Can Fly!

The manga centers on Hayabusa, a girl who is actually a god. The story begins when Hayabusa is looking intently at a man eating croquettes in a park. When the man gives her a croquette, she sprouts mechanical wings and flies away. When the man returns the next day, Hayabusa is there to thank him and offers him a ride in the sky, for which she turns into a Ki-43 Hayabusa fighter plane to do so. (Source: Anime News Network)