If you were standing on the surface of the sun, which you can't, of course, you would be whipping around at 7,000 km/h. But it rotates so slowly that it's an almost perfect sphere. The sun isn't a solid ball of rock, it's a sphere of hot plasma, so the different regions can complete their rotation at different rates. Unlike its slower poles which take 26.24 days to turn. And if you track their movements, you'll see that the sun's equator takes 24.47 days to turn once on its axis. Instead you can use a special purpose solar telescope to observe sunspots and other features on the surface of the sun.
You can't tell because staring at the sun long enough will permanently damage your eyeballs. Like all stars, our sun rotates on its axis.
Consider that fiery ball in the sky, the sun.
