Hi Kerrie,

The first measurements of the Sun's rotation were made by observing sunspots with a telescope. From what I've read the first documentation of this was probably by Thomas Harriot in 1610. The first published observations appeared in 1611 by Johannes Fabricius who observed spots for a few months. Christopher Scheiner actually measured the rotation rate of the Sun at the equator and closer to the poles of the Sun, noting that they were different in 1630.

Best,
Christina