Elkns began his football career playing for legendary Brownwood High School coach Gordon Wood. In the 1960 3A state championship game, Elkins caught a touchdown pass for the Lions to help seal a 26-6 victory over Port Lavaca. At Baylor University he continued his pass catching ways by earning All-SWC and All-American honors in 1963 and 1964. Elkins thrived under coach John Bridgers pro-style offense making 144 career receptions for Baylor for 2,094 yards and 19 touchdowns. In 1963 he led the nation and also set a SEC record with 70 receptions for 873 yards and eight touchdowns. Elkins played in the 1965 East West Shrine Game, Coaches All-American Game and was Most Valuable player of the Hula Bowl. He later played in the AFL with the Houston Oilers from 1965-1968 before injuries ended his career. Elkins was selected to the College Football Hall of Fame in 1994 and later in the Texas Sports Hall of Fame.