[2] Aktürkoğlu began his football career at Başakşehir's youth academy, signing his first professional contract with the club in 2015 at the age of 16.

Reflecting on his time at Başakşehir in a later interview, Aktürkoğlu expressed deep frustration, claiming that "four years of his life were stolen" due to a rigid hierarchy under Abdullah Avcı and Emre Belözoğlu, where senior players exercised significant authority over younger talents.

[3][4] In 2017, Aktürkoğlu sought a fresh start and joined fellow Turkish TFF Third League side Karacabey on a free transfer in search of regular playing time.

[3][4] His efforts helped Karacabey reach the promotion play-offs, but the team was eliminated by Serik Belediyespor on July 15, 2019, following a narrow 4–3 aggregate loss.

[5] His performances during the season improved, with a notable highlight being Erzincanspor's 2–0 victory over Beşiktaş in the fifth round of the Turkish Cup on 5 December 2019.

[6] He made his professional debut with Galatasaray in a 1–1 league draw against Kayserispor on 23 November 2020,[7] and scored his first goal for the club in a 3–0 win against Hatayspor on 5 December.

Before Galatasaray training started on 9 September, Marcão publicly apologized to Aktürkoğlu in front of the entire team, with the two solving their issues.

This collaboration was highlighted on 12 November when Aktürkoğlu scored a hat-trick in a 7–0 away win against his former club Başakşehir, with Icardi providing two assists for his goals.

[28] In the return fixture on 29 November, he came off the bench to score a crucial equalizer in a 3–3 home draw against Manchester United, a strike later awarded Goal of the Week for the fifth matchday of the Champions League.

[30] On 11 January 2024, he was sent off for the first time in his career, during a league match against Sivasspor for dissent after shouting at the referee, resulting in a two-match suspension.

[31] Aktürkoğlu finished the season, with 12 goals and seven assists, playing a pivotal role as Galatasaray clinched their second consecutive Süper Lig title, setting a league record of 102 points.

[33][34] On 14 September, Aktürkoğlu scored on his debut for the club, netting the opener in a 4–1 home league victory over Santa Clara.

In the process, he registered the most goals and assists (eight) for the club in his first seven matches reaching Félix Guerreiro's previous record set in the 1964–65 season.

[41] On 1 June 2021, he was named in the Turkish squad for the postponed UEFA Euro 2020, but did not make an appearance in an eventual group stage exit.

[42] He scored his first international goal on 5 September 2020 in a 1–1 home draw against Norway in a 2022 FIFA World Cup qualification match.

Actively participating in the "We Are Together" campaign, he encouraged citizens to host displaced individuals, especially in Hatay, one of the hardest-hit Turkish regions.

He also donated the match ball from his hat-trick against Başakşehir to an auction, with the proceeds aiding earthquake recovery efforts in his home country.