Francis has brought an informal, friendly style to the papacy since his election in March, including a habit of telephoning people who write to him with personal stories that catch his attention.
Alejandra Pereyra, 44, told Argentine television that at first she froze and had to ask him to repeat his name when he phoned but she felt "touched by the hand of God" when she realised she was the latest person to receive a personal call from Pope Francis.
She said the pontiff told her during the half-hour conversation on Sunday he received thousands of letters every day but her story had moved him.
Ms Pereyra wrote in her letter she felt victimised twice; once when she was raped and then when she was threatened and pressurised by investigators when she reported it. Authorities have dismissed her allegations, local press reported.
The Pope told her she was not alone and she should have faith in justice. This month Francis also called relatives of an Italian petrol station manager who was shot dead in June.