Robert Fullerton Stewart was born around 1840 in Pennsylvania. By the early 1860s, he was living in Philadelphia, Pennsylvania.
He enlisted in the Union army, and he mustered in as a private in Company G of the 22nd Pennsylvania Infantry on April 23, 1861. The regiment served at Fort McHenry in Baltimore, Maryland. He mustered out on August 7, 1861.
He returned to the army three days later, mustering in as a sergeant in Company A of the 72nd Pennsylvania Infantry. The regiment participated in the Seven Days’ Battles, the Battle of Antietam, the Battle of Fredericksburg, the Battle of Gettysburg, and the Overland Campaign. He was promoted to 2nd lieutenant in May 1863, to 1st lieutenant in September 1863, and finally to captain in January 1864. He was wounded in the ankle and thigh at the Wilderness on May 6, 1864, and he spent the next several months recovering. He mustered out on August 24, 1864.
He returned to Philadelphia after leaving the army. He applied for a federal pension in September 1864 and eventually secured one. He married Catharine Mellen in February 1870, and they adopted a son named Robert. He worked as a watchman in Philadelphia, and by 1870, he owned $500 of personal property. He died in Philadelphia on January 15, 1905.