The 21-year-old man was taken into custody on Tuesday evening, Constable Sibusiso Chauke said.
"It is alleged the rape had been taking place since March last year," he said in a statement.
"The mother of the victim confronted her on one of the days when she slept over at the suspect's place. She told the mother she is in love with him, and that they had sexual intercourse."
When the relationship continued, the mother laid a charge with the police on Tuesday.
The man was arrested at the Meadowlands Hostel. He would appear in the Protea Magistrate's Court on Thursday.