Virgil R. Carter (born November 9, 1945) is a former professional American football quarterback who played in the National Football League and the World Football League from 1967 through 1976. He was the first great quarterback from Brigham Young University. While at BYU Carter set six national, 19 conference, and 24 school records and was an academic All-American. He led BYU to its first-ever football conference championship in 1965.

Carter was drafted by the Chicago Bears in 1968 and was traded to the Cincinnati Bengals after the 1969 season. He led the NFL in pass completion percentage in 1971 and was third in overall passing. His best game of that season was the opener, in which the Bengals defeated the Philadelphia Eagles 37-14. Carter completed 22 of 30 attempts for 273 yards, three touchdowns and no interceptions. The following year he split time with Ken Anderson before Anderson took sole possession of the starting job. The Bengals chose to go with Anderson in 1973 and Carter left the Bengals for the Chicago Fire of the World Football League, where he played in 1974.

Carter was the WFL's leading passer in 1974 until an injury sidelined him in week eleven. He finished the season with 358 attempts completing 195 for 2629 yards. He threw 27 touchdown passes and was intercepted 16 times. The Fire offense in 1974 is compared today to the West Coast Offense.

In 1975 he was signed by the San Diego Chargers, then traded to the Bears during the season. He retired from the Bears after the 1976 season.

Carter was a highly intelligent quarterback, who blossomed in Cincinnati under the west coast system implemented by Bill Walsh, then the Bengals' quarterbacks coach and later head coach of the San Francisco 49ers. In his first stint with the Bears Carter earned a master's degree from Northwestern, and while in Cincinnati with the Bengals taught statistics and mathematics at Xavier University.