Yes! The Sun does rotate. But unlike the Earth, the Sun does not rotate like the solid objects (Sun is made of gaseous plasma). The Sun spins around faster at its equator than at its poles (called differential rotation). Near poles it takes up to 35 days to rotate, while at the Sun’s equator one full rotation takes only 25 days. The rotation of the Sun is important in creating complex solar magnetic fields and solar cycle. And without the complex and ever changing magnetic field there wouldn’t be huge and impressive solar eruptions, such as flares and coronal mass ejections. The rotation rate of the Sun can be calculated for example by tracking the features at the solar surface, like sunspots (not sure who did this first). Helioseismology, which studies waves in the Sun, can be used to define how the also the internal parts of the Sun’s interior rotate. Deeper inside, the Sun rotates like a solid body.