The 25-year-old has played in the World Rugby Sevens Series tournaments for Scotland having been named a core squad member at the beginning of the 2018/2019 season.
A former student at the University of Stellenbosch, South African-born Steyn has played 15s rugby in the Currie Cup for the Griquas and was named as the side's captain for their 2018 campaign.
Steyn will remain a core Scotland 7s player for the remainder of the 2018/2019 season, but will join up with Glasgow Warriors when not playing on the 7s circuit.