Aplin was born in Thetford Township, Michigan, and moved with his parents to Flint in 1848 where he attended the public schools. In the American Civil War, he enlisted on July 3, 1861, in Company C, Sixteenth Regiment, Michigan Volunteer Infantry, and served until July 16, 1865, with the rank of second lieutenant. After the war, he returned to Michigan and engaged in mercantile pursuits at Wenona (later West Bay City and now part of Bay City). He was postmaster of West Bay City from November 1869 to June 1886. He served as township clerk and township treasurer, each for three years and was a delegate to the Republican National Convention at Chicago in 1884. He was elected auditor general of the State in 1886 and 1888. He became interested in the construction of the electric railways of West Bay City and served as general manager until 1891. He was a member of the Michigan State House of Representatives in 1894 and 1895 and was again appointed postmaster of West Bay City, serving from October 1, 1898, to June 1902.

Aplin was elected as a Republican from Michigan's 10th District to the United States House of Representatives for the Fifty-seventh Congress, by special election, to fill the vacancy caused by the death of Rousseau O. Crump. Aplin served from October 15, 1901 to March 3, 1903. He was an unsuccessful candidate for renomination in 1902. He then engaged in agricultural pursuits and was also interested in the manufacture of ice. He died in West Bay City and is interred in Elm Lawn Cemetery in Bay City.