David Carr attended Valley Oak Elementary School in Fresno, California. He continued on to Fresno's Kastner Intermediate School, where he proceeded to break a number of California D-I middle school records as Quarterback for the Thunderbirds. After moving to Bakersfield, California, Carr attended Stockdale High School.
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. Carr threw 70 touchdowns versus 23 interceptions, and he won 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. Former Fresno State football player Robbie Rouse (a junior in 2011) was the last player allowed to wear the number.
With the first overall pick of 2002 NFL Draft, a new expansion team, the Houston Texans selected Carr. His 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 only the second expansion team to win its first game. Due to having a patchwork offensive line in front of him, Carr was sacked 76 times. He also set the NFL record for fumble recoveries in a single season, recovering 12 of his own. He finished his rookie year of 2002 with 2,592 passing yards, 9 touchdowns, and 15 interceptions. He also rushed for 282 yards along with 3 rushing touchdowns. The Texans finished 4-12 in their first franchise year.
In the 2003 year, Carr played 12 games (11 starts) with 2,103 passing yards, 9 touchdowns, and 13 interceptions. He also rushed for 151 yards with 2 rushing touchdowns and was sacked only 15 times. The Texans finished 5-11 in 2003.
The 2005 year began poorly as the Texans were 1-9 in their first 10 games, and plummeted to a 2–14 record to finish the year. Plagued by injuries and an ineffective offensive line that limited both the running and passing games, Carr still threw 2,488 yards while being sacked a league-leading 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 release Carr, making him a free agent for the first time of his career.
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 of Fresno. He has two brothers. His brother, Derek plays for the Oakland Raiders. Lon Boyett, his uncle, played in the NFL with the 49ers in 1978.
Carr and his wife, Melody, have three sons and one daughter.
His brother Derek has claimed that Carr has been instrumental to his preparation and training that led up to the 2014 NFL draft and has helped greatly with training and experience since being drafted by the Raiders.