Having left Crystal Palace's youth set-up in 2008, Razak joined the Manchester City Elite Development Squad in July 2010. However, he was not chosen to play his first game for the EDS until early February 2011 when he was one of the starting eleven in the EDS team that beat the Bury reserve team 2–0 at Ewen Fields in the Manchester Senior Cup. Only two days after finally making his debut for the Manchester City reserve team Razak was then given a surprise debut for the first team, coming on as a substitute for David Silva in the final minutes of the Premier League game against West Bromwich Albion on 5 February 2011. His unexpected first team debut makes Razak the ninth youth player to graduate from Manchester City's academy under manager Roberto Mancini in just over a year of the latter's management at the club. The day after his debut for the Manchester City first team Razak was added to the first team squad. In his second game for the EDS team three days later the young Ivorian was shown a straight red card for a rash challenge in the 51st minute of the Premier Reserve League North game against Bolton Wanderers.
In his second game for the Manchester City first team against Wigan Athletic on 10 September 2011 Razak was substituted on for Yaya Touré in the 80th minute of the match. He made his first full appearance for the first team on 21 September 2011 in the third round of the Football League Cup against Birmingham City, playing for 86 minutes before being substituted by Luca Scapuzzi. His second full appearance for the first team was on 26 October 2011 in the fourth round of this competition against Wolverhampton Wanderers which Manchester City won 5–2 at Molineux. Razak played in this game for 85 minutes before being substituted by James Milner. He ended that season with one league appearance as Manchester City won the 2011–12 Premier League in dramatic circumstances on the last day of the season.
On 28 October 2011, Razak was loaned to Portsmouth on a one-month deal. He made his debut for Portsmouth against Derby County the next day, coming on as a 62nd-minute substitute in a game Portsmouth lost 3–1. After one month with Pompey and three appearances, Razak returned to Manchester City and played as a late substitute in their 0–1 League Cup quarter-final victory against Arsenal at the Emirates Stadium on 29 November 2011, replacing Owen Hargreaves in the 79th minute.
On 17 February 2012, Razak, along with fellow Manchester City youngster Gai Assulin joined Football League Championship side Brighton & Hove Albion on a three-month loan deal. Razak made his debut on 22 February 2012 against Hull City, he was substituted for Gai Assulin on the 77th minute. In the next match, Razak impressed again in a 3–0 win over Ipswich Town – securing man of the match on his Falmer Stadium debut. Seagulls midfielder Gary Dicker recovered from injury quicker than expected and it was felt that opportunities for Razak would be extremely limited so the Ivorian rejoined Manchester City.
On 29 September 2012, Razak joined Charlton Athletic on a three-month loan deal. On 29 October 2012, he returned to Manchester City having made only two first team appearances.
On 2 September 2013, Razak joined Russian club Anzhi Makhachkala on a season long loan deal, with a trigger clause that once he made an appearance for Anzhi the transfer becomes a permanent one.
On 17 October 2013, it was announced that Razak had moved to Anzhi Makhachkala permanently after the clause in his contract, that once he'd made an appearance for Anzhi the deal become permanent, had become activated.
On 30 January 2014, Razak joined West Ham United on a short-term contract. In April 2014 he left the club without having played a first team game.
On 5 January 2017, Razak announced on his Instagram account that he had signed a 3-year deal with Swedish team IFK Goteborg.
Razak made his début for the Côte d'Ivoire national football team against Russia in a friendly match in August 2012. He was included in the Côte d'Ivoire squad for the 2013 Africa Cup of Nations and was in Les Éléphants' starting line up for their third group match against Algeria.FA Community Shield (1): 2012
As of match played 4 December 2014
As of 14 August 2013