Because the sun is not a planet, a solar day is undefined. The definition of a solar day is the amount of time it takes for a planet to rotate on its axis before the sun returns to the same spot in the sky.
The sun does rotate on an axis, so a day in terms of 24 hours can be defined. Because the sun is not a rigid body, this rotation is differential, so it is difficult to define a rotational period. The sun spins more slowly at the equator than at it's poles. It takes 27 days for the equator to complete a rotation and 31 days for the poles to spin once.