Exum attended Deep Run High School in Glen Allen, Virginia, where he participated in football, basketball and track. In 2008, he was named first-team All-region and was a first-team selection for the Richmond Times-Dispatch All-Metro defensive team. As a junior, he threw for 860 yards and rushed for 658 yards, scoring 25 total touchdowns, while also adding 20 tackles and three interceptions as a defensive back. He accounted for 2,357 all-purpose yards and 30 total touchdowns in his senior season, including six on returns. He also lettered in basketball and track at Deep Run. In 2009, he earned first-place finishes in both the 100 meters and 200 meters at the Douglas Freeman Meet. He also posted a personal-best time of 23.16 seconds in the 200-meter dash at the district meet, where he placed sixth. Considered a three-star recruit by Rivals.com, Exum was listed as the 38th best athlete prospect of his class and the No. 14 player in the state. He was rated the No. 16 prospect in Virginia by The Roanoke Times. He was rated the No. 42 athlete prospect nationally by both ESPN.com and Scouts Inc. He was also ranked the No. 69 quarterback prospect in the nation by Scout.com.
College career
Exum attended Virginia Tech from 2009 to 2013. In 2009, he redshirted as a true freshman. In 2010, Exum played in all 14 games, starting five. He played at free safety but moved around a lot in the Hokies nickel defense. He recorded 45 tackles and had a team-high nine pass breakups for the season. In 2011, he was an honorable mention All-ACC selection at safety, after he led the team with 89 tackles, while adding five tackles for loss, 1.5 sacks and an interception on the season. He also had 10 pass breakups, two quarterback hurries, two forced fumbles and a fumble recovery. In 2012, Exum was moved to cornerback in spring practice. He started all 13 games, recording 48 tackles, including 1.5 for loss and led the team with five interceptions. He also had 16 pass break-ups, 21 Passes Defended two forced fumbles and a fumble recovery. He capped off his season with an MVP performance in the 2012 Russell Athletic Bowl vs Rutgers, and was also named second-team All-ACC. In January 2013, Exum suffered a torn ACL and lateral meniscus of his right knee during a pick-up basketball game. Before his injury, he was wildly considered to be one of the shutdown players of the season. Especially considering he had 5 interceptions and 16 pass break-ups and his 21passes defended as his first year at the Cornerback position. He missed the team's spring practice and fall camp due to the injury, but was cleared to play on October 1, 2013 by surgeon Dr. James Andrews, just under nine months since his initial diagnosis. Despite being cleared to play, Exum opted not to dress the next two games, but returned to start the next three games before spraining his ankle which caused him to miss the rest of the season, including the Sun Bowl vs. UCLA Exum and his highly touted NFL prospect teammate, Kyle Fuller, also missed the Sun Bowl.
Professional career
Pre-draft
Minnesota Vikings
After trading down twice from 148th and 168th, the Minnesota Vikings drafted Exum in the sixth round of the 2014 NFL Draft. Many analysts stated that, had he stayed healthy all year, he most likely would have been a 1st–2nd round pick. Exum became the first safety drafted by the Vikings since the club selected Harrison Smith 29th overall in the 2012 NFL Draft. He was also the highest selected defensive back of the 3 picked by the Vikings in the 2014 NFL Draft.
2014 season
Exum played in 15 games with no starts during his rookie campaign, contributing heavily on special teams. He was tied for 5th on the team with 7 special teams tackles, compiling 3 of them in the final 4 games of the season. He finished the season with 6 tackles.
2015 season
Exum was one of just two Vikings defenders to play every snap in the 20–10 win over the Atlanta Falcons in Week 12, and he had a strong day in his first career start as the Vikings contained wide receiver Julio Jones and the Falcons' fifth-ranked pass offense. Exum gave up only 16 yards in two passes targeted for him, knifed in to stop Tevin Coleman for a four-yard loss at the goal line and recovered Anthony Barr's forced fumble on Coleman's 46-yard run. Exum ended the game with three tackles and a fumble recovery. In Minnesota's Week 13 loss against the Seattle Seahawks Exum tackled Seahawks running backThomas Rawls to force his first career fumble in the NFL.
2016 season
Exum was waived/injured by the Vikings on August 30, 2016. He was then placed on injured reserve after clearing waivers.
2017 season
After an injury in mini-camp, Exum went into the 2017 training camp healthy, and spent the first week of practice as a nickel corner after spending his first few seasons as a safety. He was waived by the Vikings on September 16, 2017.
On November 7, 2017, Exum signed with the San Francisco 49ers.
2018 season
On June 6, 2018, Exum re-signed with the San Francisco 49ers. He was released on September 1, 2018, and was re-signed again on September 3, 2018. In Week 4 against Philip Rivers and the Los Angeles Chargers, Exum recorded his first career interception and touchdown. On March 14, 2019, Exum re-signed with the 49ers.
2019 season
On August 31, 2019, Exum was released but re-signed the next day. He was released on October 2, 2019. He was re-signed on December 4, 2019. On January 1, 2020, Exum was waived by the 49ers.