Born in Cincinnati in 1843, he enlisted, June 15, 1861, with the 47th Ohio Infantry, Company A, in Cincinnati. Captured outside of Atlanta, he was imprisoned in the notorious Andersonville Prison Camp for two months and four days. Geiger was discharged August 11, 1865 in Little Rock, Arkansas. He reenlisted with Troop M, of the 7th U.S. Cavalry, November 29, 1867 in St. Louis, Missouri. Geiger completed his enlistment and was discharged November 29, 1872 in Unionville, South Carolina. Nineteen days later, in Louisville, Kentucky, he reenlisted with the 7th Cavalry and was attached to Troop H, December 18, 1872. He completed his service and was discharged, for medical reasons, at Ft. Buford, South Dakota, December 18, 1877. Geiger is described in military records as having been dark complexioned, gray eyes, 5' 5" in height. He could read and write. Military records identify him as a Protestant. Geiger was admitted multiple times to the Dayton, Ohio VA hospital for various service-related illnesses ranging from chronic dysentery to rheumatism, beginning in 1897. He died January 23, 1904, age 61. Geiger was married. He was survived by his half brother, Edward Metzer, 1208 W. 7th Street, Cincinnati, Ohio. Geiger was interred in the Dayton National Cemetery, Montgomery County, Ohio, Section N, Row 20, Grave 47.
Sergeant George Geiger was one of twenty-four soldiers of the 7th Cavalry to earn the Medal of Honor during the Battle of the Little Big Horn on June 25, 1876, often called "Custer's Last Stand." Five men received awards for direct combat actions. Sergeant Geiger was one of nineteen men who was cited for heroism in obtaining critical water for the wounded. Along with Private Charles Windolph, Blacksmith Henry Mechlin, and Saddler Otto Voit, Sergeant Geiger took up an exposed position outside of the cavalry's line of defense in order to draw enemy fire away from fifteen other men who risked their own lives to get water from the river. For four hours the four valiant troopers, acting as both decoys and an attacking force, dodged bullets and laid down a protective covering fire. They accomplished their mission so well that not one of the men who dashed the eighty yards from the cavalry encampment to the river was killed.