Swope enlisted and served during World War I as captain of infantry. He was elected as a Republican to the Sixty-sixth Congress by special election, to fill the vacancy caused by the death of Harvey Helm (August 1, 1919 – March 3, 1921). He was an unsuccessful candidate for reelection to the Sixty-seventh Congress in 1920.
Swope was appointed aide-de-camp with the rank of colonel on the staff of Governor Edwin P. Morrow in 1919, before resuming the practice of law. He was the chairman of the Republican executive committee of Fayette County, Kentucky, from 1928 to 1931, and was appointed and subsequently elected a judge of the circuit court of the twenty-second judicial district of Kentucky and served from 1931 to 1940. He was the unsuccessful Republican nominee for Governor of Kentucky in 1935 and 1939. He was a delegate to the Republican National Convention in 1936, 1940, and 1944, and was chairman of the Republican State convention in 1936. He was also a member of the judicial council of Kentucky from 1931 to 1940. He died in Lexington, Kentucky, in 1961 and was buried at Lexington Cemetery.