As a true freshman in 2010, Morris appeared in six games with four starts. He finished the season completing 82 of 153 passes for 1,240 yards with seven touchdowns and nine interceptions. As a sophomore in 2011, he appeared in five games with one start. He completed 26 of 37 passes for 283 yards with two interceptions. As a junior in 2012, he entered the season as the starting quarterback and started all 12 of the Hurricanes games. On September 29, 2012, in a game against NC State, he set the ACC record for passing yards in a game with 566. He finished the season completing 245 of 421 passes for 3,345 yards with 21 touchdowns and seven interceptions. As a senior in 2013, he passed for 3,028 yards and 21 touchdowns. He finished his career with 7,896 yards with 49 touchdowns and 30 interceptions.
Professional career
Jacksonville Jaguars
Following the 2014 NFL Draft, Morris was signed as an undrafted free agent by the Jacksonville Jaguars. The Jaguars released Morris on August 29, 2014. He was signed to the practice squad on August 31, 2014. He was released on September 4, 2015.
Philadelphia Eagles
Morris was claimed off waivers by the Philadelphia Eagles on September 6, 2015. He was released on September 21, 2015, but re-signed with their practice squad on September 22.
Indianapolis Colts
On December 24, 2015, Morris was signed to the active roster of the Indianapolis Colts. On September 7, 2016, he was released by the Colts. He was signed to the practice squad the following day. He was elevated to the active roster on November 23, 2016, after starting quarterback Andrew Luck suffered a concussion. On December 1, 2016, he was waived by the Colts and was re-signed to the practice squad the next day. Morris signed a reserve/future contract with the Colts on January 2, 2017. He was waived September 3, 2017.
Washington Redskins
On January 2, 2018, Morris signed a reserve/future contract with the Washington Redskins. He was waived on April 9, 2018.
Seattle Seahawks
On April 13, 2018, Morris signed with the Seattle Seahawks. He was waived on May 11, 2018.
Houston Texans
On May 14, 2018, Morris was claimed off waivers by the Houston Texans. He was waived on August 16, 2018.
Orlando Apollos
On November 27, he was protected by the Apollos in the second round of the Pick or Protect QB Draft. He was cut on January 30, 10 days prior to the start of the AAF's inaugural season.