He took his oath Tuesday at the Capitol, surrounded by his wife and children.
The optometrist won a Nov. 27 special election to fill a vacancy in District 19, entirely in DeSoto County.
He'll serve the final three years of a four-year term started by Republican Merle Flowers of Southaven, who resigned to spend more time with family.
Parker jokingly told his colleagues to be patient as he learns their names.
The Senate usually has 52 members. There are two vacancies now because of the recent deaths of Democratic Sens. Bennie Turner of West Point and Alice Harden of Jackson.