Curry transferred from Liberty University to Duke after the 2008–09 season. Per transfer rules, Curry sat out the 2009–10 basketball season. At Duke, he also chose to wear his family number 30.
Curry competed for the United States in the 2009 FIBA Under-19 World Championship in New Zealand, winning the tournament by defeating Greece 88–80 in the final. For the tournament, Curry averaged 9.0 points, 2.2 rebounds and 1.1 assists per game.
As a redshirt sophomore, Curry was named a starter after a toe injury sidelined Kyrie Irving. In a game against Miami (Ohio), Curry led the team with 17 points on 57% shooting. He scored a season high 22 points against North Carolina on February 9, 2011. On December 29, 2012, he scored a career-high 31 against Santa Clara. At the end of his senior year, Curry was named to the All-ACC first team and was named a second team All-American by Sporting News.
On November 1, 2013, Curry was acquired by the Santa Cruz Warriors of the NBA Development League as an affiliate player. On November 22, in his D-League debut, Curry recorded 36 points on 12-of-19 shooting, as well as 6 assists and 3 rebounds. On December 24, he signed with the Memphis Grizzlies. On January 5, 2014, Curry both made his NBA debut and was waived by the Grizzlies. Four days later, he was reacquired by the Santa Cruz Warriors.
In July 2014, Curry joined the Orlando Magic for the Orlando Summer League and the Phoenix Suns for the Las Vegas Summer League. On September 29, 2014, he signed with the Magic. On October 7, 2014, Curry's D-League rights were acquired by the Magic's affiliated team, the Erie BayHawks, in a trade with the Santa Cruz Warriors. This was done in preparation for Curry returning to the D-League following training camp, as the Magic were now able to send him to their affiliated team instead of Curry returning to Santa Cruz. As anticipated the Magic waived Curry at the conclusion of training camp on October 25, and five days later he was acquired by the Erie BayHawks for the start of D-League training camp. In his debut for Erie in the team's season opener on November 14, Curry scored 23 points on 9-of-24 shooting in a win over the Idaho Stampede. On February 4, 2015, he was named to the Futures All-Star team for the 2015 NBA D-League All-Star Game for the second time in his career.
On March 11, 2015, Curry signed a 10-day contract with the Phoenix Suns. He made his Suns debut later that day in a 106–97 win over the Minnesota Timberwolves. He was not offered a second 10-day contract by the Suns following the expiration of his first on March 21, and subsequently returned to the BayHawks. In 43 games for Erie in 2014–15, he averaged 23.8 points, 3.9 rebounds, 4.2 assists and 1.4 steals per game.
On July 15, 2016, Curry signed with the Dallas Mavericks. He made his debut for the Mavericks in their season opener on October 26 against the Indiana Pacers. In 16 minutes off the bench, he recorded seven points, three rebounds, one assist and three steals in a 130–121 overtime loss. On November 8, he scored a then career-high 23 points in a 109–97 win over the Los Angeles Lakers. He tied that mark on November 21, scoring 23 points with five three-pointers as a starter in a 96–91 loss to the San Antonio Spurs. Curry missed four games in early December with a right knee sprain. On January 29, 2017, he had career highs of 24 points and 10 rebounds to lead the Mavericks to a 105–101 win over San Antonio. On February 24, 2017, he set a new career high with 31 points in a 97–84 loss to the Minnesota Timberwolves. Three days later, he had a 29-point effort to go with five three-pointers in a 96–89 win over the Miami Heat.
On October 7, 2017, Curry was ruled out indefinitely after being diagnosed with a stress reaction of his left tibia. On February 6, 2018, he was ruled out for the entire season after it was determined he required surgery on his left tibia.
