Acord was born to parents who were Utah pioneers and members of The Church of Jesus Christ of Latter-day Saints, Valentine Louis Acord and Mary Amelia Acord (née Pedersen), in the ranching area called Prattville, just west of the town of Glenwood, Utah. Art's father was of German and English descent. The Acord family descends from a Prussian mercenary soldier of the American Revolutionary War whose name was Eckert. Art's paternal grandmother was a descendant of Frances Latham, an early settler of New England. Art's mother, who was of Danish descent, died when Art was just 19 months old while the family was living in the Stillwater, Oklahoma area. The Acord family had moved there for the mother's health and took part in the September 28, 1891 Oklahoma Land Run. She died a few weeks later on November 28, 1891. After her death, the family moved back to Utah. As a young man, Acord worked as a cowboy, ranch hand and rodeo contestant. In 1912, he won the World Steer Wrestling (Bulldogging) Championship at the Pendleton Round-up and won that same World Championship title again in 1916, defeating challenger and friend Hoot Gibson.