Alexander Crawford Gwin was born around 1836 in Pennsylvania to Alexander and Sarah Gwin. His father was a millwright who owned $700 of real estate in 1850. The family lived in Antis, Pennsylvania, until the 1850s, when they moved to Logan, Pennsylvania. His father died in the 1850s. By 1860, he was working as a farmer, and he owned $500 of real estate and $150 of personal property.
He enlisted in the Union army on April 20, 1861, and he mustered in as a private in Company B of the 3rd Pennsylvania Infantry later that day. According to his service records, he was 5 feet, 11 inches tall, with light hair and gray eyes. The regiment mustered out three months later, on July 29, 1861. Gwin rejoined the Union army soon afterward. He enlisted on September 18, 1861, and he mustered in as a sergeant in Company F of the 76th Pennsylvania Infantry on October 28. He died in the assault on Fort Wagner in Charleston Harbor on July 18, 1863.