He started his professional football career at Inter Allies in the First Capital Plus Premier League. In 2013–14, Aidoo was nominated in the category "Defender of the year" in the Ghana Premier League, but eventually missed out on the award. Aidoo was the club captain during the season of 2014–15.
In August 2015, Swedish team Hammarby in Allsvenskan signed Aidoo on a six-month loan deal. He made his debut, and his only appearance during the season, against then reigning champions Malmö FF on 25 October 2015. Even though Hammarby lost with a score of 0–1, Aidoo put on an impressive performance being voted "Hammarby player of the game". Before the 2016 Allsvenskan season, he signed for Hammarby permanently on a three-year deal. He made his first league appearance of the season against Malmö FF on 18 May, playing the first half before being substituted at halftime. Mid through the campaign, manager Nanne Bergstrand chose to swap the two central defenders, with Aidoo and newly signed David Boo Wiklander making their entrances as regular starters. Out of the following 11 games, Hammarby won an impressive 7 – also keeping a clean sheet in 6 consecutive away fixtures. Aidoo scored his first competitive goal for Hammarby on 12 September 2016, in a 1–1 draw against Örebro SK on home turf. Aidoo started out the 2017 season in fine form, with Hammarby only conceding 5 goals in the 6 first matches. Aidoo's performances led to him being named in April's best eleven for African players over the world, in the magazine Goal.
On 24 July 2017, Aidoo completed a transfer to Genk in the Belgian First Division A. He signed a three-year contract with the club, with an option for a further. The transfer fee was reportedly set between €1.25 million and €2 million. He made his debut for the side on 26 August, coming on as a late substitute, in a 1–0 home win against Mechelen. Aidoo scored his first goal for Genk in a 1–0 win against the domestic giants Anderlecht on 22 October, and was also voted as the "man of the match". Between 23 September and 19 November, Genk went on an eight matches long unbeaten streak in the league, with Aidoo starting all of the fixtures.
Celta
On 11 July 2019, Aidoo agreed to a five-year contract with Spanish La Liga side RC Celta de Vigo for a reported fee of €8 million. His former club Hammarby received €380,000 as part of the deal. He made his debut for the Galician club on 24 August 2019 in a 1-0 home win against Valencia, starting and playing 90 minutes at center-back.
