The 25-year-old has played eight games for the national side and has represented South Africa at several age levels.
Since joining the Soweto-based outfit in 2013, Erasmus scored 13 goals in 51 games for the Pirates.
Rennes are fourth in France's Ligue 1 and their new coach Rolland Courbis is targeting a second-placed finish for the current campaign behind runaway leaders Paris Saint-Germain.