Kokorin made his debut for the senior FC Dynamo Moscow team on 4 October 2008 – Dynamo was decimated by injuries and was losing to FC Saturn Moscow Oblast 0–1 at the halftime when Kokorin came on as a substitute. With 18 minutes to go Kokorin scored an equalizer (Dynamo went on to win 2-1). He became the youngest player to score a goal for Dynamo in the Russian Premier League (17 years 199 days). He scored a winning goal in a 1–0 victory over FC Lokomotiv Moscow in his second game as a starter on 3 November 2008.

On 29 July 2009, he scored the winning goal in a 1–0 win against Celtic F.C. in the first leg of their third qualifying round tie in the UEFA Champions League in Glasgow.

Kokorin was a part of the Russia U-21 side that was competing in the 2011 European Under-21 Championship qualification. Kokorin was called up to the Russia national football team for a friendly against Greece in November 2011 and made his national team debut in that game on the 11th, a 1–1 draw in Piraeus. He played two games at UEFA Euro 2012 as Russia failed to pass the group stages.

He scored his first national team goal on 11 September 2012 in a 2014 FIFA World Cup qualifier against Israel, which finished as a 4–0 victory at the Ramat Gan Stadium.

On 4 July 2013, Kokorin agreed personal terms with Anzhi Makhachkala after the club had triggered his €19 million release clause. He was officially signed by Anzhi and registered with the league as an Anzhi player. However, before he could play a single official game for Anzhi (he was out of commission due to injury at the time of his signing), on 6 August, following restructuring of Anzhi at business level, the whole squad was put up for sale, including new signing Kokorin. The next day, Yuri Zhirkov, Igor Denisov and Kokorin were all transferred to Dynamo for an undisclosed fee.

On 2 June 2014, he was included in Russia’s 2014 FIFA World Cup squad. He scored Russia’s goal in their 1–1 final group match draw with Algeria, as the team was knocked out by the North African side.

Kokorin scored three times in Russia’s successful UEFA Euro 2016 qualifying, concluding on 12 October 2015 with a penalty in their last game, a 2–0 win over Montenegro at the Otkrytie Arena which sealed Russia’s place at the expense of Sweden. He was selected in Russia’s squad for Euro 2016, playing in all three matches as Russia finished bottom of the group.

On 30 January 2016, he moved from Dynamo to FC Zenit Saint Petersburg.

On 9 April 2016, Kokorin scored his first goal for Zenit in a game against FC Amkar Perm.

On 15 March 2018, he suffered an ACL tear in a Europa League game against RB Leipzig and missed the 2018 FIFA World Cup as a result.

On 7 October 2018, Kokorin and Krasnodar midfielder Pavel Mamayev assaulted a Russian government official in a restaurant. The football players struck the official with a chair and used racial slurs. Kokorin and Mamayev were caught on camera hitting the official in a cafe in Moscow, according to Gazeta. It quotes a Russian lawyer saying that a conviction such as this would carry a maximum sentence of five years. Hours before that incident, Mamayev, Kokorin and other young people were involved in an altercation with the driver of a Channel One show presenter; he received brain damage, nose fracture and face contusions after numerous punches. Kokorin was apprehended for two months. Kokorin remained in prison until his trial which began on 9 April 2019. On 8 May 2019, he was sentenced to 1-year-6-month in penal colony. Considering the time he spent in pre-trial detention, the latest possible date for his release from custody was considered to be 14 December 2019. He was paroled on 17 September 2019.

According to his lawyer Yuri Padalko, following his release from penal colony on 17 September 2019, he signed a new contract with Zenit until the end of the 2019–20 season.

On 21 January 2020, Russian Premier League club PFC Sochi announced that Kokorin will join them on loan until the end of the 2019–20 season. He initially refused to report and was moved to Zenit-2. He eventually agreed to the loan and it was confirmed by Zenit on 17 February 2020.

On 19 June 2020, Kokorin scored a hat-trick in the first match back following the suspension of the Premier League due to COVID-19 pandemic. The match was a notable 10–1 victory over FC Rostov. Rostov were forced to play their youth side though after their senior and reserve sides, 43 players in total, were forced to quarantine.

On 2 August 2020, Spartak Moscow announced the signing of Kokorin to a three-year contract, with the option of an additional year, after his Zenit St.Petersburg contract had expired.