He currently plays for Norwich City, wearing the number 29 shirt. He plays primarily as a Forward. He stands at 186cm tall and weighs 80kg. His current market value is estimated at 5M €.

His most recent move was a Free from Brondby IF to Norwich City on 2024-08-24. The reported fee was 2.5M €.

In the English Football League Championship 2025-2026 season, Oscar Schwartau scored 3 goals and provided 1 assists across 31 appearances, averaging 0.1 goals per game with 30 shots attempted and 13 on target.