Aaron Burr was born around 1827 in Charlottesville, Virginia. He was born into slavery and was owned first by Dabney Gouch and then by Paul Hill Goodloe. Goodloe took Burr to Louisiana, where he sold him to New Iberia planter Charles C. Weeks. He lived on the Alic Plantation near Jeanerette, Louisiana, and married Mary Ann Gray, who died in Houston sometime during the war.

Burr enlisted as a private in the Union army on October 22, 1863, in New Iberia. He mustered in to Company F of the 93rd USCT Infantry Regiment in New Orleans on November 20. His service record describes him as 5 feet, 8 inches tall, with black hair, black eyes, and black complexion. He was eventually transferred to Company F of the 81st USCT Infantry Regiment, and on May 26, 1865, he received a promotion to first sergeant. On July 1, however, the army consolidated the 93rd USCT and 81st USCT regiments and reduced Burr to a private. He was promoted to corporal on September 10, 1866, and returned to the rank of first sergeant on October 16.  Burr served throughout Louisiana and performed daily duty as the company cook. He mustered out on November 20, 1866, in New Orleans. 

Following the war, Burr worked as a blacksmith, and possibly a sharecropper, on the Losiel Plantation in Jeanerette. He married Reita Madison in 1866. It is unclear whether his two children, Lucy and Henry Burr, whose birth dates are not known, were from his first or second marriage. Later in life, he suffered from senile disability and a hernia, and in 1903 he began receiving a $6 per month pension. Burr died on April 19, 1906, of unknown causes.