The 32-year-old man was arrested on Wednesday, but the girl told police during her statement that she was in a relationship with the man, Constable Mhlbunzima Mvelase said.
Beeld newspaper reported on Thursday that the girl was found on Wednesday with the man on his parents’ plot in De Deur.
The girl’s mother told the Afrikaans daily that she ran away from her home in Randhart, Alberton, on June 28.
Ritual candles, CDs containing instructions on witchcraft, as well as pornography, were found at the plot.
Elmarie Potgieter from People Search and Rescue Unit, told Beeld the man admitted that he and the 13-year-old performed protective spells and other rituals together.
The man’s parents said they were unaware that he was living with an underage girl.
Potgieter told Beeld the man’s mother knew he lived with his girlfriend, but he told them they could not meet her because she had “issues”.
The man would appear in the Vereeniging Magistrate’s Court on Thursday.