[1][2][3] Oduro was part of the Accra Lions youth development programme until he reached the first team during the 2022/23 season.
He has played 50 games in the Ghanaian Premier League since his debut on 20 November 2022 when he was sixteen years, scoring one goal in a 1-1 draw against Bibiani Gold Stars.
He was signed to FC Barcelona Atlètic for the 2024–25 season where he will be playing with his countryman Abdul Aziz Issah.
[9] He promised Barcelona fans not to disappoint them and said his coming with fire because is always his dream to play in the first team and he will work hard to get there.
[14] On 6 November 2024, David Oduro made his first debut game for Barca Athletic against Real Sociedad B.