On Saturday afternoon, Kwame Poku scored in Peterborough United's 2-1 win against Oxford United in the EFL League One. The former Colchester United player scored in the 31st minute to make it 2-0 for his team. Billy Bodin, though, scored in the 52nd minute to cut his team's deficit to 1-2 and put an end to the game at home. The 21-year-old midfielder has played in seven games for Peterborough United this year, scoring once and assisting three in the League One this season. On 2 August 2021, he signed a four-year contract with Peterborough United. Poku scored his first Peterborough goal in a 3-2 win against Milton Keynes Dons on 1 October 2022. Poku was called up to the Ghana national football team for the first time on 19 March 2021,  for the 2021 Africa Cup of Nations qualifying games against South Africa and São Tomé and Príncipe. He made his debut on 28 March 2021 after coming on as a 79th-minute substitute for Mohammed Kudus in a 3–1 victory over São Tomé and Príncipe at the Accra Sports Stadium.