He attended the common schools and Wilbraham Academy in Massachusetts. He also studied at Wesleyan University, located at Middletown, Connecticut, where he studied Law.
In 1859 he entered the law office of Wells & Strong as a law student. He was admitted to the bar in 1862 and practiced in Hartford. Buck served as assistant clerk of the State House of Representatives in 1864 and clerk in 1865. He served as clerk of the Senate in 1866; as president of the Hartford Court of Common Council in 1868; as City attorney 1871 — 1873; as Treasurer of Hartford County 1873 — 1881 and as a member of the State Senate in 1880 — 1881.
Buck was elected as a Republican to the Forty-seventh Congress (March 4, 1881—March 3, 1883) and to the Forty-ninth Congress (March 4, 1885—March 3, 1887). He was an unsuccessful candidate for re-election in 1882 to the Forty-eighth Congress and for the re-election in 1886 to the Fiftieth Congress.
Elected to represent Connecticut's 1st District in the United States House of Representatives, serving from 1881 to 1883. Also served as a Member of the Connecticut State Senate in 1880.
On April 12, 1865, Buck married Mary A. Keeney of Manchester, Connecticut. They had two children, Florence K. and John Halsey.