Cudjoe started his career with Great Somas in Accra till he transferred to Sunyani based a Division Two club Young Apostles, managed by Ghanaian football administrator Samuel Anim Addo.
[2][6] Cudjoe was scouted and later signed up by Addo after he had competed in the maiden edition of the BabyJet U-16 tournament at the Asamoah Gyan Sports Complex in Accra Academy.
[11][5] On 22 December 2019, he won his first trophy with the club, after Asante Kotoko defeated their rivals Hearts of Oak by 2–1 victory in the President's Cup.
[15][16][17] He scored his debut Ghana Premier League goal in a home match against Ebusua Dwarfs, helping Asante Kotoko to secure a 2–0 victory.
[25][26] Cudjoe was signed on season long loan deal by Accra-based team, Legon Cities FC.
[29][30] On 17 November 2021, Scottish Premiership team Dundee United announced the signing of Cudjoe subject to international clearance, upon approval of his Visa application.