Swift was recruited by his former coach at Richmond, John Kingston, to join the Connacht-based club Galwegians in June 2000. He made his first appearance for the Connacht provincial team against Ulster in the same year, while still playing for Galwegians in the All-Ireland League. Swift also played for Connacht in the 2000–01 European Challenge Cup, making his European debut for the province on 7 October 2000 as a replacement against Béziers at home, before starting in both the return match on 13 January 2001 and the game against Neath the following week.
