The 24-year-old's twitter account boasts of 23 million followers and her Facebook has nearly 60 million friends, helping her edge out Lady Gaga, who came second with 28 million Twitter followers and 53 million Facebook fans.
Rihanna and Gaga are very open and provocative about their professional and personal life on the social networking site.
Rapper Eminem is third on the list as he has the highest number of Facebook followers, surpassing 60.3 million while pop star Justin Bieber comes fourth.
The list mostly compromises of musicians, with the magazine theorizing that music stars adopted social media platforms earlier than their film and TV counterparts.
Singer-actress Selena Gomez (No 10) is the only actress on the list, and Portuguese footballer Cristiano Ronaldo (No 7) is the only athlete to be crowned a social networking superstar.