In 2013, Rivkin withdrew from the Holon Grand Prix due to an illness. She returned to competition at the 2013 Thiais Grand Prix, where she finished 5th in all-around and won a bronze in the ball final. At the 2013 Pesaro World Cup, Rivkin finished 4th in all-around, and won another bronze in the ball final. She won the silver medal in ball (tied with Sylvia Miteva of Bulgaria) at the Sofia World Cup. Rivkin finished 7th in all-around at the 2013 Minsk World Cup, and won a bronze medal in the hoop final. She then competed at the 2013 European Championships in Vienna, Austria. She qualified for the event finals, and finished 6th in hoop and 7th in ball. At the 2013 Summer Universiade in Kazan, she finished 5th in all-around ahead of Korean Son Yeon-Jae. She won the all-around gold medal at the 2013 Maccabiah Games in Jerusalem, Israel. She finished 11th in All-around at the 2013 World Cup series in St. Petersburg, Russia. Rivkin finished 10th at the 2013 World Championships All-around final.