Annan joined Bologna in 2020. He became a key figure in their Primavera squad, featuring in many games between 2020 and 2022. Annan was first called up to the senior team in August 2021 during Bologna's 2021–22 preseason tour. Ahead of Bologna's
Coppa Italia game against
Ternana he was called up again in the process making his professional debut in that game on 16 August 2021, starting and playing 56 minutes before being substituted for
Musa Barrow as Bologna lost by 5–4. He was subsequently named on the bench for their Serie A match against
Salernitana on 22 August. On 22 January 2022, he made his Serie A debut after coming on for
Arthur Theate in the 66th minute in their 2–1 defeat to
Hellas Verona. Annan played for Italian
Serie C club
Imolese in the 2022–23 season. On 7 July 2023, Annan joined
Serbian SuperLiga club
Novi Pazar on a one-year loan with an option to make the move permanent at the end of the 2023–24 season. In June 2024, Red Star Belgrade signed Annan on a three-year contract, with an option to extend for an additional year. Before the start of the season, he was loaned to newly promoted
OFK Beograd on a one-year deal. In January 2025, Annan returned to Red Star Belgrade following a productive loan spell at OFK Beograd, where he made 19 appearances and made four assists. Upon his return, he quickly established himself as a key figure in the squad, contributing significantly to Red Star's successful campaign to secure the
2024–25 Serbian SuperLiga title. This triumph marked the first major silverware of Annan's professional career.
Saint-Étienne On 7 August 2025, Annan signed for
Ligue 2 club
Saint-Étienne on a three-year deal. ==International career==