Truax attended Holy Cross, where he received All-Prep honors and was a highly regarded prospect. He also practiced basketball, baseball and track. He accepted a football scholarship from Louisiana State University. He became a starter as a sophomore and was mainly used as a blocker for running backEarl Gros, tallying 5 receptions for 61 yards. As a junior he blocked for running back Jerry Stovall, registering 3 receptions for 101 yards and one touchdown. In his last year he was named a team captain, while leading the team with 10 receptions for 112 yards and one touchdown. He also played defense during his career, collecting 2 interceptions and 3 fumble recoveries.
Truax was selected by the Cleveland Browns in the second round of the 1964 NFL draft. He also was selected by the Houston Oilers in the second round of the 1964 AFL Draft. As a 21-year-old rookie, he was converted into an outside linebacker and suffered a torn a hamstring on the first day of training camp. He lost 6 weeks and was traded to the Rams without having played a down for the Browns on September 5, in exchange for a second round draft choice.
In 1964, he was tried at defensive end before settling at tight end. In his first 2 seasons he played mainly on the special teams units. In 1966, he began playing in the offense, where his size made him an excellent blocker. In 1967, he recorded 37 receptions for 487 yards and 4 touchdowns. In 1968, although he played with a broken bone in his left wrist, he tallied 35 receptions for 417 yards and 3 touchdowns. In 1969, he had 37 receptions for 431 yards and 5 touchdowns. In 1970, he registered 36 receptions for 420 yards and 3 touchdowns On May 19, 1971, Truax was traded along with wide receiverWendell Tucker to the Dallas Cowboys in exchange for wide receiver Lance Rentzel.
Dallas Cowboys
In 1971, he was limited with leg injuries and was able to start in 10 games, with 4 contests started by Mike Ditka. He only had 15 receptions for 232 yards and one touchdown, but was a part of the Cowboys' Super Bowl VI championship team. In 1972, he was coming from off-season knee surgery and was only able to play in 6 games and catch 4 passes for 49 yards. On September 5, 1973, he was assigned to the taxi squad because of a stomach disorder and was eventually placed on the injured reserve list.