Scobee was born in Longview, Texas. He played youth soccer, including outstanding play on the high school team and as part of a competitive league team. He began kicking for the football team his senior year at Longview High School. In addition to handling the kicking duties, Scobee was also the punter. He was 23-for-23 on extra points and was six for nine in the field goal category. He was well known for kicking kick-offs through the uprights. He earned first-team All-District honors as a kicker and second-team All-East Texas accolades as a punter in recognition of his successful season.
The Jacksonville Jaguars selected Scobee with the 137th overall pick in the fifth round of the 2004 NFL Draft. In the 2004 season, he led the team with 93 points after connecting with 24-of-31 field goals and 20-of-21 of his extra points. In addition, he ranked 13th in the AFC in field goal percentage and tied for third on touchbacks with 11 on 58 kickoffs. During his first five NFL seasons, he was named AFC Special Teams Player of the Week four times. On January 5, 2008, In the Wild Card Round playoff game against the Pittsburgh Steelers, Scobee made the game winning 25-yard field goal. One week later, in the Divisional round, he converted on both of his field goal attempts, kicking a 39-yard and a 25-yard field goal. However, the Jaguars lost to the New England Patriots 31-20. In 2008, during a game against the Indianapolis Colts, Scobee hit a 51-yard field goal to give the Jaguars a 1-2 record, then one week later, he booted a 37-yarder in overtime to beat the Texans. In week 8, Scobee tied his career record with a 53-yard field goal against Cleveland. In Week 4 of the 2010 season, Scobee made a 59-yard game-winning field goal on the final play of the game to beat the Indianapolis Colts by a score of 31-28, breaking his previous record of 53 yards. The 59-yard field goal set a new franchise record for the Jaguars. For his performance he earned the AFC Special Teams Player of the Week award. On October 24, 2011, Scobee kicked four field goals to lead Jacksonville to a 12-7 victory over the Baltimore Ravens on Monday Night Football. Three of his field goals were over 50 yards in length, including two field goals of 54 yards each. Scobee's three 50+ yard field goals tied an NFL record for most 50+ yard field goals in a single game with five other kickers including Neil Rackers, Morten Andersen, and Sebastian Janikowski. On July 16, 2012, Scobee agreed to a four-year deal with the Jacksonville Jaguars after receiving a franchise tag earlier in the year. Scobee would remain with the Jaguars through the 2014 season.
Pittsburgh Steelers
On August 31, 2015, Scobee was traded to the Pittsburgh Steelers for a sixth-round pick in the 2016 NFL Draft. He was Pittsburgh's third kicker of the preseason after Shaun Suisham and Garrett Hartley suffered season-ending injuries. He made his debut in the Steelers' Week 1 game against the New England Patriots, missing his first two field goal attempts, before scoring an extra point and two field goals in the Steelers' 28–21 loss. In the Steelers' Week 4 game against their AFC North rival Baltimore Ravens, the Steelers led 20–17 late in the fourth quarter. Scobee missed two field goals—a 49-yarder and later a 41-yarder—in the closing minutes. The Ravens then kicked a field goal to tie the game at 20, sending the game to overtime. Ravens kicker Justin Tucker made a 52-yard field goal on the Ravens' next drive to hand the Steelers a 23–20 overtime loss. Two days later, the Steelers released Scobee, signing Chris Boswell as his replacement.