Russell F. Wright was born around 1834 in Lewis County, New York. By the early 1860s, he was living in Manchester, New York, and working as a wagon maker.
He enlisted in the Union army on August 30, 1862, and he mustered in as a private in Company K of the 148th New York Infantry on September 14. According to his service records, he was 5 feet, 9 inches tall, with light hair and grey eyes. He was promoted to corporal on January 1, 1863. He was wounded in the right side near Yorktown, Virginia, on December 16, 1863, but he eventually recovered and rejoined the regiment. He died in the Second Battle of Fair Oaks on October 27, 1864.