That giant flaming star in the sky does rotate, but moves at a much slower pace than the Earth.
It takes 24 hours for the Earth to make a full rotation, but since the sun isn’t a solid object like a planet, its rotation is harder to pinpoint.
“Since the sun is a ball of gas/plasma, it does not have to rotate rigidly like the solid planets and moons do,” according to NASA.
Dispatches From The Front 