No it does not.

The Sun does rotate, but it does not rotate like the Earth.

That’s because, despite its fluid centre and atmosphere, the Earth rotates (more or less) like a rigid body, all of it rotating at (again: more or less) the same speed. 1 day is 24 hours, no matter where on (or in) the Earth you are.

The sun, however, is manifestly not a rigid body. It is a gigantic ball of superheated plasma, which means that different parts of the sun rotate at different rates.

The equator of the sun completes a full rotation once every 24.5 days, whilst the poles take almost 38 days to complete a rotation.

It can be a little bit difficult to spot with the naked eye, but you can just about appreciate the difference in speeds of the sunspots in this video:

Modern helioseismology has also provided significant evidence that the rate of rotation inside sun also varies hugely — so the surface can rotate up to 40% faster than the material halfway between the core and the surface!

Hence, the sun does rotate, but nothing like the Earth!