Earlier in his career, Rasmussen played two games in the 1997 ICC Trophy.

The following year, he played in the 2001 ICC Trophy in Ontario.

He played in the ICC Trophy between 1994 and 2001 and generally occupied the upper-middle order.

He also played in the ICC Trophy between 2001 and 2005.

He also played in the 2001 ICC Trophy in Ontario.

He played in the 1997 ICC Trophy, which was held in Malaysia.

He then played in the ICC Trophy later that year.

He next played for them in the 2001 ICC Trophy in Ontario.

He went on to play in the 1997 ICC Trophy too.

He also played in the 2001 ICC Trophy, which was his last international appearance.