Immediately following graduation, he entered the United States Marine Corps and served in the Pacific Theatre during World War II.
The other Senate seat from South Carolina was held at the time by the Democrat-turned-Republican Strom Thurmond, who had been elected as an Independent write-in candidate in 1954 and as a Democrat in 1960 but switched to the GOP in 1964 to support Barry M. Goldwater for the presidency.
Parker did not challenge Thurmond in the Republican primary but instead attempted in a special election for a two-year term to succeed former senator Olin D. Johnston, who died in office in 1965.
Despite his twin defeats by Hollings for the U.S. Senate, Parker remained committed to the newly invigorated South Carolina Republican Party as well as the national GOP.
He died at the age of eighty-six at Oconee Medical Center in Seneca, South Carolina, after experiencing a year of declining health.