Yes, the sun does rotate on its axis, just like Earth does, but the rate is different. One day on Earth takes 24 hours. One day on the sun takes an average of 27 days. You can see that spin in this video, made of images from the Solar Dynamics Observatory. A group of sunspots is visible in the video, with a comparison to the size of Earth.
https://www.nasa.gov/feat...ot-turn-toward-earth