In 2016, Rivkin began her season competing at the 2016 Grand Prix Moscow finishing 17th in the all-around. On February 26–28, Rivkin competed at the 2016 Espoo World Cup finishing 5th in the all-around. In apparatus finals; she placed 5th in hoop, ribbon, 6th in ball, and 8th in clubs. On March 17–20, Rivkin for the first time was able to stand on the all-around podium in a World Cup event held at the 2016 Lisboa World Cup winning the all-around bronze. On May 13–15, Rivkin competed at the 2016 Tashkent World Cup finishing 4th in the all-around (71.350) after throwing her ribbon out of the carpet on her last routine, Rivkin qualified to 3 apparatus finals: taking silver in ball, bronze in hoop and placed 8th in clubs. She finished 5th in the all-around at the 2016 Minsk World Cup. Rivkin suffered an ankle injury and withdrew from the 2016 European Championships, she was replaced by Linoy Ashram. On July 22–24, culminating the World Cup of the season in 2016 Baku World Cup, Rivkin returned to competition where she finished 7th in the all-around with a total of 71.200 points, she qualified to 2 apparatus finals taking bronze in ball and 4th in ribbon.