After growing up in Athens, Georgia, but playing high school football in Arlington, Virginia at Washington-Lee High School, Scott played college football at the University of Georgia, where he led Georgia in interceptions in 1967 with six interceptions and 1968 with ten interceptions. In 1967, Scott was named first-team All-SECdefensive back by the Associated Press, and in 1968 again in both the AP and the UPI. The ten interceptions in a season is now second-most in Georgia history behind Terry Hoage’s 12 in 1982. Scott’s 175 return yards on interceptions in 1968 is also second all-time for Georgia.
Scott’s college career total of 315 interception return yards is the most in Georgia’s history. He also holds the current Georgia record for career interceptions.
Scott was inducted into the State of Georgia Hall of Fame in 1986 and the Athens (GA) Athletic Hall of Fame in 2000.
It was announced on May 17, 2011 that Scott had been selected for induction into the College Football Hall of Fame.
Scott left the University of Georgia after his sophomore year to go to Canada and play professional football in the CFL. Based on his 20 July birth date, Scott's military draft lottery number of record was 187. The highest administrative draft number called for Scott's year group was 195, suggesting that Scott could have been, but was not, drafted for military service during the Vietnam War.
Scott began his professional career in 1969 in the Canadian Football League as a defensive back and kick returner with the BC Lions. He was drafted by the Dolphins in seventh round of the 1970 NFL Draft, where in his rookie year, he recorded five interceptions and returned one punt return for touchdown. The following year, he recorded seven interceptions and 318 punt return yards, helping the team reach Super Bowl VI, which they lost 24-3 to the Dallas Cowboys. Scott recorded a 21-yard punt return in the game.
Scott was a key member of the 1972 Miami Dolphins undefeated season, and was named Super Bowl MVP of Super Bowl VII, recording two interceptions in the Dolphins' 14-7 win over the Washington Redskins including one in the fourth quarter. He helped the Dolphins in their 24-7 Super Bowl VIII win, recording two fumble recoveries, 20 punt return yards, and 47 kickoff return yards in that game. He established 2 Super Bowl Records. Jake set a record by being the first player to recover 2 fumbles in one game. He also first established the record for most career fumble recoveries in Super Bowls at two, a record now shared by 12 others. Scott is still the only player to have recovered one of his own team's fumbles and one of his opponent's fumbles.
Overall, Scott finished his nine seasons with 49 interceptions. He made 35 interceptions playing 6 seasons for Miami, making him the Dolphins' all-time leader in that category,. Scott had 13 fumble recoveries in his career. On special teams, he gained 1,357 yards and a touchdown returning punts, and 137 yards on six kickoff returns.
Scott played for the Redskins the final 3 years of his career.
In the late 1980s, NFL Films named Scott as the Dolphins All-Time Neutralizer sponsored by Tums. He was inducted into the Georgia-Florida Hall of Fame in 1998.