Murry played college basketball at Wichita State University, leading the Shockers to the second round of the 2012 NCAA Men's Division I Basketball Tournament and winning the 2011 National Invitation Tournament. Murry averaged 12.1 points, 4.8 rebounds and 3.3 assists per game during his senior season in 2011–12.
After going undrafted in the 2012 NBA draft, Murry joined the Los Angeles Lakers for the 2012 NBA Summer League. He spent August and September in Turkey and Israel before returning to the United States. On November 2, 2012, he was selected with the 15th overall pick by the Austin Toros in the 2012 NBA Development League Draft. Three days later, he was traded to the Rio Grande Valley Vipers. During his rookie season, he played 52 games in total for the Vipers, averaging 9.0 points, 2.8 rebounds, 3.0 assists and 1.8 steals per game.
In July 2013, Murry joined the Houston Rockets for the Orlando Summer League and the New York Knicks for the Las Vegas Summer League. On September 11, 2013, he signed with the Knicks. On January 29, 2014, he was assigned to the Erie BayHawks. He was recalled the next day. On January 31, 2014, he was reassigned to the BayHawks. He was recalled the next day. In 51 games for the Knicks in 2013–14, he averaged 2.7 points and 1.0 assists per game.
On August 28, 2014, Murry signed with the Utah Jazz. On November 13, 2014, he was assigned to the Idaho Stampede. He was recalled by the Jazz on December 2, reassigned on December 31, and recalled again on January 3. He went on to make his Jazz debut later that night. The next day, he was waived by the Jazz and on January 10, he was reacquired by the Rio Grande Valley Vipers.
On March 12, 2015, Murry signed a 10-day contract with the Washington Wizards. He signed a second 10-day contract with the Wizards on March 22 but was released halfway through his contract on March 27, and returned to the Vipers three days later. He was subsequently deactivated by the Vipers and did not play for the team again in 2014–15.
In July 2015, Murry joined the Washington Wizards for the 2015 NBA Summer League, but was limited to just two total minutes of action due to a right groin injury. He later re-signed with the Wizards on September 25, 2015, only to be waived again by the team on October 24 after appearing in four preseason games.
On October 31, 2015, Murry was acquired by the Texas Legends in a trade with the Vipers. On November 13, he made his debut for the Legends in a 104–82 loss to the Austin Spurs, recording 10 points, five rebounds and seven assists in 39 minutes.
On March 4, 2016, Murry was traded to the Sioux Falls Skyforce in exchange for the returning player rights to Andre Dawkins. On March 11, he made his debut for the Skyforce in a 121–117 win over the Canton Charge, recording 12 points, three rebounds, four assists and one block in 24 minutes off the bench. He helped the Skyforce finish with a D-League-best 40–10 record in 2015–16, and went on to help the team win the league championship with a 2–1 Finals series win over the Los Angeles D-Fenders, his second D-League title.
In July 2016, Murry joined the Minnesota Timberwolves for the 2016 NBA Summer League. On September 26, 2016, he signed with the Timberwolves, but was waived on October 22 after appearing in three preseason games. On December 5, he signed with Yeşilgiresun Belediye of the Turkish Super League. On February 3, 2017, he parted ways with Yeşilgiresun.
On July 24, 2017, Murry signed with German club ratiopharm Ulm for the 2017–18 season.