Robert P. Archer was born around 1818 in Amelia County, Virginia, to John and Fanny Archer. His father earned a living as a farmer. He lived in Amelia County, and by 1850, he was also working as a farmer. He moved to Powhatan County, Virginia, in the 1850s. He married Sally W. Archer on May 22, 1857, but she died on March 18, 1859. By 1860, he was working as a planter, and he owned $20,000 of real estate and $40,000 of personal property.
He served as a major in the Confederate Quartermaster Department during the Civil War. After the war, he worked as a tobacconist in Virginia. In early 1878, Governor Frederick Holliday appointed Archer an honorary commissioner to the Exposition Universelle in Paris, France. According to newspaper reports, he planned to “give a practical exhibition of the process of manufacturing Virginia tobacco.” Before he could depart, however, he died suddenly of erysipelas in Richmond, Virginia, on March 18, 1878.