Carr began as the starting quarterback at Fresno State during the 2000 and 2001 seasons after redshirting in 1999. While he was quarterback, the Bulldogs went 7-5 and 11-3. In his senior season the team beat Colorado, Oregon State, and Wisconsin, all members of BCS conferences. There was speculation about whether the Bulldogs would qualify for a BCS bid, something then unprecedented for a Mid-major team. They climbed to as high as number 8 in the polls, and Carr was on the cover of Sports Illustrated. During his collegiate career Carr completed 587 of 934 passes for 7,849 yards. He threw 70 touchdowns versus 23 interceptions. Carr collected the Johnny Unitas Golden Arm Award during his senior year.
On September 1, 2007, the Fresno State Bulldogs retired Carr's #8 jersey in his honor. Current Fresno State football player Robbie Rouse, a Junior in 2011, is the last player who will be allowed to wear the number.
With the first overall pick of 2002 NFL Draft, the expansion Houston Texans selected Carr. He started all but four games for the team in its first five years. Carr's professional career began on a productive note. The Texans played their first regular season game on September 8, 2002, defeating the Dallas Cowboys, 19–10, at Houston's Reliant Stadium. Houston became just the second expansion team to win their first game. The Texans won four games that season. Due to having a patchwork offensive line in front of him, Carr also became the most sacked quarterback in a single season of the NFL, being sacked 76 times. He also set the NFL record for fumble recoveries in a single season (recovering 12 of his own). With Carr under center, the Texans improved in each of the next two years, finishing 5–11 in 2003 and 7–9 in 2004. Carr's 2004 season was his best statistically, as he finished with his highest career passer rating and threw for over 3,500 yards.
In 2005, the Texans won only one of their first ten games, finishing the season with a 2–14 record. Plagued by injuries and an ineffective offensive line that limited both the running and passing games, Carr still threw for over 2,500 yards while being sacked 68 times. Despite the drop-off, the Texans exercised an option in Carr's contract that extended him for three years.
The Texans finished the 2006 season at 6–10. For the season, Carr posted a completion percentage of 68.9% (a career high) and tied the single-game NFL record of 22 consecutive pass completions (against the Buffalo Bills). However, new Texans general manager Rick Smith decided to go in a different direction at quarterback. Thus, the Texans acquired Matt Schaub from the Atlanta Falcons and decided to part ways with Carr.
Carr is considered to be one of the biggest quarterback busts in NFL history since 1980, and was ranked 10th on Fox Sports' list of worst No. 1 overall picks in NFL Draft history.
Carr agreed to terms with the Carolina Panthers on April 6, 2007. Following an injury to starting quarterback Jake Delhomme, Carr was named the starter. He played in six games (started four games) and had three touchdowns and five interceptions, with a 53.7 completion percentage and a passer rating of 58.3. Carr suffered a back injury during the fifth game of the season (a victory vs. the New Orleans Saints) on a sack by Will Smith, and saw limited action during the remainder of the 2007 season, being replaced by Vinny Testaverde and Matt Moore. He was released on February 27, 2008.
On March 12, 2008, Carr signed a one-year contract with the New York Giants, reuniting with former Houston offensive coordinator Chris Palmer. Subsequently, the Giants released former backup quarterback Jared Lorenzen. Carr backed up Eli Manning for two seasons. In the 2009 offseason, Carr was re-signed to a one-year, $2 million contract on February 9, 2009. In his two years with the Giants, Carr saw action in seven games and threw three total touchdown passes.
Carr was put into the 49ers Week 7 game against the Carolina Panthers after Smith suffered a shoulder injury. Carr struggled completing only 5 of 13 passes for 67 yards and throwing a crucial interception late in the 4th quarter.
Carr is the son of Rodger and Sheryl Carr. He has two brothers, one of whom (Derek) is a quarterback at Fresno State, as Carr was. Lon Boyett, his uncle, played in the NFL with the Raiders and 49ers in the early 1980s.
Carr and his wife Melody have three sons and one daughter.