Born in Houston, Alworth was raised in Brookhaven, Mississippi, where he played football at Brookhaven High School before attending the University of Arkansas. While in high school, he earned fifteen letters. Alworth's sister Ann was fast enough in the 50 and 75-yard dash in track to be invited to the Olympic Games trials, though she declined the invitation. After high school, Alworth was offered contracts by New York Yankees and the Pittsburgh Pirates. At Arkansas, the six-foot (1.83 m), 180-pound (82 kg) Alworth was a flanker who led all colleges in punt return yardage in 1960 and 1961. He also was a track star, running the 100 and 200-yard dashes (in 10.6 seconds and 21.2 seconds, respectively) and long jump. Alworth was a three-time Academic All-American, graduating with a degree in marketing as a pre-law student. In 1962, Alworth was on multiple All-American teams: Look magazine, Associated Press, United Press International and Coaches. He is a member of the Pi Kappa AlphaFraternity. Alworth is a member of the University of Arkansas Hall of Honor and the Arkansas Sports Hall of Fame; he was named to the University of Arkansas' 1960's All-Decade Team, and the school's All-Century Team in 1994.
He was taken 8th overall in the first round of the 1962 NFL draft by the San Francisco 49ers. The American Football League's Oakland Raiders drafted him as their first pick (ninth overall) in the second round of the 1962 AFL draft, and then traded his rights to the San Diego Chargers in return for halfback Bo Roberson, quarterback Hunter Enis, and offensive tackle Gene Selawski. Alworth opted to sign with the Chargers instead of the 49ers. The Chargers moved Alworth to wide receiver. His slender build, speed, grace, and leaping ability earned him the nickname "Bambi."
He held records for the most consecutive games with a reception (96), most seasons with over 1,000 receiving yards (7) and still holds the record for the most games with 200+ yards receiving (5) and was the only receiver to average more than 100 yards a game in three consecutive seasons (1964–1966). He remains the fastest player in AFL/NFL history to reach 4,000 (42 GP), 5,000 (52 GP), 6,000 (62 GP), 7,000 (73 GP), 8,000 (83 GP) and 9,000 (97 GP) receiving yards in his career. Alworth formed a formidable tandem with Chargers quarterbackJohn Hadl, and is considered by many to be the best wide receiver in all professional football during the 1960s. He was one of the few American Football League stars to be featured on the cover of Sports Illustrated (SI), which like other media of the 1960s, showed a distinct bias for the NFL. SI even went so far in 1969 as to declare Alworth "Pro Football's Top Receiver", this, a year before the AFL-NFL merger, and two years before the Common Draft, before which many claimed the AFL had inferior players.
In Super Bowl VI, he caught a touchdown pass for the Cowboys in a 24-3 victory over the Miami Dolphins. Alworth would later call the two receptions he made in Super Bowl VI (one that converted a third and long and the other for the touchdown) the two most important catches of his career.
Alworth finished his 11 AFL/NFL seasons with 543 receptions for 10,266 yards. He also rushed for 129 yards, returned 29 punts for 309 yards, gained 216 yards on 10 kickoff returns, and scored 87 touchdowns (85 receiving and 2 rushing).
In 1999, he was ranked number 31 on The Sporting News' list of the 100 Greatest Football Players, making him the highest-ranking Charger and the highest-ranking player to have spent more than one season in the AFL.