Autrey began his motorcycle racing career in 1964 competing in flat track racing at Perris Auto Speedway. In 1968 he recorded his first significant victory when he won the 100cc class in the Rosarita Grand Prix in Mexico, competing in off-road racing. He was also active in road racing during this period, placing second in the novice road race class held before the 1971 Daytona 200.
In 1972, Autrey finished second in the United States Speedway National Championship. That same year, after attending the 1972 Individual Speedway World Championship at Wembley Stadium in London, he resolved to concentrate fully on speedway racing.
In 1973, Ivan Mauger recommended Autrey to the Exeter Falcons in England, a club with which he would remain for seven years. The move proved transformative for his career, and he became one of the most prominent American speedway riders of his era.
Autrey's breakout moment on the world stage came at the 1976 Individual Speedway World Championship, held at the Silesian Stadium in Chorzów, Poland, where he finished ninth with seven points. This result made him the first American to reach the speedway world final since Ernie Roccio in 1951, a distinction that brought considerable attention to American speedway prospects.
His finest World Championship result came in 1978, when he finished third at the World Final held at Wembley Stadium in London, scoring 11 points plus a further three points in the run-off for the bronze position. In the same year he also competed in the World Longtrack Final at Mühldorf, finishing eleventh with nine points.
In 1980 Autrey moved to the Swindon Robins, and that year the United States team competed in the World Team Cup at Wrocław's Olympic Stadium, where the USA finished as runners-up, scoring 29 points (with Autrey contributing nine). From 1981 to 1982 he rode for the Poole Pirates.
In 1982, Autrey was a member of the United States team that won the World Team Cup at White City Stadium in London. His teammates were Bruce Penhall, Bobby Schwartz, Kelly Moran, and Shawn Moran, and the team scored 34 points in total. Autrey retired from speedway at the end of the 1982 season, at the relatively young age of 29.
After retiring from motorcycle competition, Autrey transitioned to automobile racing and competed as a NASCAR driver. He made one start in the Winston Cup Series, in 1985, beginning from 29th on the grid in a 41-car field before retiring late in the race with transmission trouble, finishing in 34th place.
Autrey also competed part-time in the Winston West Series, making eleven starts and recording four top-ten finishes across that campaign.
Autrey's 1976 World Final appearance marked a turning point for American participation in speedway at the highest level. His bronze medal at the 1978 World Final remains one of the best individual performances by an American in the championship, and his contribution to the USA's 1982 World Team Cup victory represents the pinnacle of American speedway on the global stage during that period.