Police said the 19-year old exchange student was with a South African male friend when they were attacked at one of the city's attractions, the 300-metre-high Signal Hill.
They were forced into their car and ordered to drive to a nearby residential area known as Summer Greens.
"En route to Summer Greens, the female was raped by both suspects," regional police spokesman Andre Traut told AFP.
The couple were also robbed of their personal effects.
No arrests have been made yet.
South Africa has one of the world's highest incidences of rape, with estimates that a woman is raped every few minutes.
Official statistics show that around 65,000 sexual offences were committed in South Africa in 2012 alone.