A native of Miami, Burns attended Miami Northwestern High School, where he played defensive back and was a teammate of current Steelers teammate wide receiver Eli Rodgers, Vikings Quarterback Teddy Bridgewater, and Raiders wide receiver Amari Cooper. As a junior, playing safety, Burns made 80 tackles, 10 for losses. He also broke up 87 passes, caused 17 fumbles, and made 22 interceptions. Regarded as a four-star recruit by Rivals.com, Burns was listed as the No. 15 cornerback prospect in his class.
He committed to Miami, where the Hurricanes hoped to pair him with Tracy Howard on the outside.
He was an All-USA high school track and field team selection by USA Today in 2011 and 2012. At the 2011 USA Youth outdoor track and field championships, Burns won both the 110 meter hurdles (13.90),and the 400 meter hurdles (52.23). At the 2012 Bob Hayes Invitational, Burns broke records in the 110 hurdles (13.35) and the 300 (36.14), both originally set by Michael Timpson in 1985. His 110 hurdles time was the second-fastest worldwide by a youth athlete in 2012, behind only Wilhem Belocian's 13.29 at the 2012 World Junior Championships in Athletics in Barcelona. In 2012 Burns had the No. 5 time in the World (No. 1 in USA) in the 110 meter hurdles amongst junior athletes (under 20). In 2014 Burns broke the American junior record in the indoor 60 meter hurdles, breaking a 38-year-old record.
Coming out of the University of Miami, Burns was projected by analysts to be a first or second round pick. He attended the NFL Combine but was unable to complete all the drills after suffering a knee injury. He stood on his combine numbers at the Miami Hurricane's Pro Day, but chose to redo the vertical and added two inches while completing the other drills he was unable to perform at the combine. He worked out with 12 other Miami Hurricanes in front of representatives from a total of 31 teams, including Steelers' head coach Mike Tomlin. Although his Pro Day numbers were hampered by a torrential down pour, he was able to proceed and complete his drills. After his workout, general managers from three teams commented that he is a top cornerback prospect.
The Pittsburgh Steelers selected Burns with the 25th overall pick in the 2016 NFL Draft. He was the first cornerback selected by the Pittsburgh Steelers in the first round since Chad Scott was selected 24th overall in 1997 NFL Draft.
On June 8, 2016, the Steelers signed him to a four-year, $9.59 million rookie contract with a $5.17 million signing bonus.
He started the season as the third cornerback behind veterans William Gay and Ross Cockrell. On September 12, 2016, he made his professional debut against the Washington Redskins. On October 16, 2016, Burns made a season-high 5 solo tackles during a 15-30 loss to the Miami Dolphins. The following game, he made four solo tackles during a loss against the New England Patriots. Burn's was promoted to the starting nickel back position for the sixth game of the season after fellow rookie Sean Davis played in the slot for the first five games.
On November 6, 2016, Burns started his first career game against the Baltimore Ravens and intercepted a pass by Joe Flacco in the first quarter. He was named the starter over William Gay and his interception was the first of any Steeler's defensive back of the season. The following game, Burns recorded six combine tackles in a 35-30 loss to the Dallas Cowboys. In a Week 11 matchup with the Cleveland Browns, he made three solo tackles and intercepted Cody Kessler's pass on the Brown's first drive, helping the Pittsburgh Steelers win 24-9. On December 4, 2016, Burns recorded a season-high six solo tackles and an assisted tackle during a 24-14 win over the New York Giants. The next game, the Pittsburgh Steelers defeated the Buffalo Bills and Burns made three solo tackles and intercepted Tyrod Taylor for his third pick of the season. On January 1, 2017, he racked up a season-high eight combined tackles and deflected a pass as the Steelers defeated the Cleveland Browns 27-24.
He finished his rookie season with a total of 65 combined tackles, 13 pass deflections, and three interceptions in 16 games and nine starts. Burns started the last seven games of the season as the Steelers' outside cornerback opposite Ross Cockrell, with veteran William Gay covering the slot. on January 8, 2017, Burns started in his first career postseason games and recorded three solo tackles and one assist in the Pittsburgh Steelers' 30-12 AFC Wildcard game victory over the Miami Dolphins.
Burns was born to Artie Tyrone Burns and Dana Smith and was raised in Miami, Florida. On October 24, 2006, his father was arrested in South Carolina for trafficking cocaine and was sentenced to 25-years in prison. His father's projected release date is May 24, 2027. His mother died from a heart attack at the age of 44 in October 2016. The University of Miami's digital department raised $40,000 through a GoFundMe account for his mother's medical expenses. Burns also has a one-year-old son named A.J. with his girlfriend of three years, Ella, and has two younger brothers, Jordan, age 14, Thomas, age 16.
On February 25, 2015, his brother, Thomas Burns, committed to play football for his alma mater, the University of Miami.
On June 30, 2017, Burns was arrested in Miami, Florida for driving with a suspended license.