Branscomb was born in Newmarket, New Hampshire on June 16, 1822. He grew up to attend Phillips Academy in Exeter before attending Dartmouth College, where he graduated in 1845. Subsequently, he studied law at the Cambridge Law School, was admitted to the bar, and practiced for six years in Holyoke, Massachusetts. Upon the organization of the Emigrant Aid Society, Branscomb became one of its agents. He came to Kansas in July 1854 and went up the Kansas River as far as Fort Riley to select a location for a town, but finally agreed with Dr. Charles Robinson on the site of Lawrence.
On July 28, 1854, he conducted the pioneer party of 30 persons sent out by the society to Lawrence, where they arrived on August 1. The second party, also conducted by Mr. Branscomb, arrived in October. He continued to act as an agent for the aid society until 1858, when he permanently settled in Lawrence and opened a law office. He immediately began to take an active part in the political life of the territory; he was elected to the Territorial House of Representatives and was a member of the Leavenworth Constitutional Convention.
In 1874, Branscomb returned to Lawrence, and in 1886, he ran for Kansas governor as the Prohibition Party nominee, coming in third.
Blackmar, Frank W.; Kansas: A Cyclopedia of State History, Vol I; Standard Publishing Company, Chicago, IL 1912.