Jordan and both of his parents were born in Barbados; his maternal grandparents are British citizens. After initially being educated at Combermere School in Bridgetown, Barbados where he studied alongside singer Rihanna, he gained a sporting scholarship to complete his formal education at Dulwich College, in England.
Jordan made his 1st XI debut for Surrey versus Middlesex at Lord's in August 2007. He took 2–41 on his first-class debut and in his second match, versus Durham, helped to dismiss the home side by taking 3–42. He received the NBC Denis Compton Award as Surrey's most promising young player in 2007.
After suffering a stress fracture of the back, Jordan was unable to play in the 2010 English cricket season. He resumed training in December that year.
At the end of the 2012 season, Jordan was released by Surrey after six years with the county. He returned to Barbados to play a second winter season for the Barbados national cricket team, before joining Sussex for the English 2013 season, taking championship best figures of 6–48 on debut against Yorkshire.
Qualified to play for both the West Indies and England (through both maternal genealogy and residency), he chose to play for England. He made his ODI debut in September 2013 against Australia, and took his first ODI five-wicket haul against Sri Lanka on 28 May 2014 at Old Trafford, with figures of 5 for 29, helping England to a 10-wicket win.
Jordan was named in the England Test squad for their series against Sri Lanka, before making his debut in the first Test.
He was also named in the 3rd, 4th and 5th Test matches of India's tour of England in 2014.
Jordan made his ODI debut against Australia, taking figures of 3-51. Jordan's selection had come as a surprise to many following his injury problems. Jordan played in the first two matches of the return series in Australia, taking 1-50 and 2-53. Jordan played in the final three games of the series, the pick of his figures being 2-37 in the final game of the series. Jordan's economy rate did not pass 6.00 runs per over in any of the games, making him one of England's stand out bowlers.
Jordan made his T20 debut at the World Cup against New Zealand in a rain affected match. He took 2-28 in the second match against Sri Lanka as England secured an unlikely victory. Jordan played in the defeat against South Africa which ended their hopes of progressing in the competition. He took 1-13 in three overs against the Netherlands but was unable to prevent an embarrassing defeat for England.
In the first match of the ODI series against Sri Lanka, Jordan excelled, taking 3-25 and smashing 38 off just 16 balls. This earned him the man of the match award. Jordan took 5-29 in the third match of the series as England cruised to victory. Jordan was expensive in the fourth match, managing 2-67 as Sri Lanka won the match to take the series into a decider. In the final match he took 1-55 as England lost the game and the series 3-2. Jordan was called up to the test team to face Sri Lanka following his impressive performances. In the first test, he took 5 wickets in the match but was unable to force a victory as the match ended in a draw. He was less impressive for the second match, failing to take a wicket as England lost by 100 runs.
Jordan was selected in the squad for the first test against India, but missed out as Ben Stokes returned from injury. He was also named in the squad for the second test. He played in his first game of the series in the third Test. He did not take a wicket in the match, but kept his place for the next match of the series. Here he was again not at his best, although he did take three wickets to help England go 2-1 up in the series. In the final test of the series, Jordan took 3-32 in the first innings, before making 20 with the bat. With England in a commanding position he took 4-18 in the second innings to help England win the match and the series 3-1. He played in the second ODI against India, although he did not perform well, finishing with figures of 0-73. He did not play again in the series.
Jordan was selected in the squad for the return series against Sri Lanka. He made his first appearance of the tour in the third ODI, where he took figures of 2-46. He took 2-35 in the next game, although England lost. In the fifth ODI he took another two wickets to keep England's hopes of winning the series alive. He proved expensive in the next game, finishing with figures of 2-68. He ended he tour by taking another two wickets, although England again lost to lose the series 5-2.
Jordan only played once in England's tri series against India and Australia, taking figures of 1-33 in the first match of the tournament against Australia. He made 17 with the bat but England suffered defeat. This proved to be Jordan's only game of the series.
Jordan was overlooked at the start of the World Cup and did not play until England met Bangladesh in a must win game. Jordan took figures of 2-59 as Bangladesh posted 275. Jordan was later run out for a duck as England failed to chase the target and were eliminated. In the final game against Afghanistan Jordan picked up the man of the match award after picking up figures of 2-13 to help England win by nine wickets.
Jordan kept his place in the team for the tour of West Indies. In the first innings of the first Test, he remained unbeaten on 21. After taking 1-46 in the first innings, he took 1-48 in the second innings as England were unable to force a result. In the second Test he took 2-65 in West Indies first innings and followed this up taking a wicket in the second innings to help England win the game. In the third Test he was less effective. He failed to take a wicket in the West Indies first innings as they were bowled out for 189. After England collapsed in their second innings, Jordan took 1-24 in the West Indies second innings but England lost the game by five wickets as the West Indies levelled the series at 1-1.
Although Jordan didn't play in the Test series, he returned to the fold for the ODI series. He picked up figures of 1-33 in the first match, as England secured an emphatic victory. However, he was expensive in the next match, taking figures of 1-97 as New Zealand posted 398 to secure a win on the D/L method. Jordan injured himself in the match and was ruled out of the rest of the series, which England went on to win 3-2.