Ransom Campbell was born around 1827 in Cape Vincent, New York. He married a woman named Susanna in the late 1840s, and they had at least three children: Rachel, born around 1850; Alden, born around 1855; and Harriet, born around 1858. They lived in Cape Vincent, and Campbell worked as a laborer. He spent two years in Auburn Prison, from April 20, 1855, until April 20, 1857, for an unnamed crime.
He enlisted in the Union army on October 14, 1861, and he mustered in as a corporal in Company A of the 94th New York Infantry later that day. He was eventually reduced to the ranks for an unknown offense. He was wounded in the Second Battle of Bull Run on August 30, 1862, and he was transferred to the Invalid Corps on September 1, 1863. He remained devoted to the Union cause. As he explained in September 1862, "I do not wish to see the day that the south shall be recognized as a government for our only hopes of a lasting peace must be in conquoring the enemys of our country." He mustered out on December 1, 1863. He returned to Cape Vincent after leaving the army, and he died there on May 26, 1869.