Following graduation, Dickey was drafted in the third round of the 1971 NFL Draft by the Houston Oilers, where he played four seasons. Dickey started ten games with the Oilers, winning two overall, including Houston's lone win in the 1973 season.
In 1976 he was packaged in a trade to the Green Bay Packers involving John Hadl. Dickey led the Packers to the playoffs in the strike-shortened 1982 season. The Packers won the opening round after Dickey went 19 of 26 (73%) for 286 yards with 4 touchdowns and no interceptions in a 41-16 triumph over the St. Louis Cardinals. Green Bay was eliminated the following week by the Dallas Cowboys in the divisional round after Dickey went 24 of 37 for 274 yards with 1 touchdown and 3 interceptions as the team fell 37-26.
Perhaps the high point of Dickey's NFL career came in 1983 when he powered the Packers' offense to a then-team record 429 points. His 4,458 yards that season served as the team record until being surpassed by Aaron Rodgers in 2011, and threw a career-best 32 touchdowns, the most in the NFL in 1983. Dickey was named second-team All-NFC behind Joe Theismann. Dickey's Packers had beaten Theismann's Super Bowl champion Washington Redskins in a thrilling Monday Night Football game earlier that season (Washington kicker Mark Moseley missed a field goal in the closing seconds, preserving the Packers' 48-47 win). The game remains the highest aggregate score in MNF history.
Dickey retired from professional football after the 1985 season. He holds Packers records for highest completion percentage in a game with a minimum of 20 attempts (19-21, 90.48%, versus New Orleans on December 13, 1981). His record for most passing yards in a regular season game (418 versus Tampa Bay on October 12, 1980 was broken by Matt Flynn on Jan. 1, 2012 with 460 yards. (Aaron Rodgers had 422 in a playoff game against the Arizona Cardinals); and highest average gain in a season (9.21 yards per attempt in 1983). The latter is an NFL single-season record for quarterbacks with 400 or more attempts.
After retiring from football, Dickey relocated to the greater Kansas City area where he opened a football-themed restaurant. After a business partner was found to be unethical, he left the restaurant business for a career in public relations. Dickey has four grown daughters; Natalie, Meredith, Elizabeth and Paloma Guastello who was previously married to George Guastello of Leawood Kansas, and resides in Leawood, Kansas. He then worked for the popular Kansas City AM station Sports Radio 810 on the show "Crunch Time", airing at 9:00 a.m. He now works at Serve You, a Pharmacy Benefit Management company home based in Milwaukee, WI. Then worked at MBPI in Lee's Summit as an accountant.