Stochastic rotation of rotating pairs in a hexagonal superlattice pattern is observed in a dielectric barrier discharge system. It is found that the pairs rotate with orientation and diameter randomly changing by observing a series of frames recorded by a high speed video camera. Frames recorded by a high speed framing camera with an exposure time corresponding to current pulse phases in one half cycle of the applied voltage show that one rotating spot, six small spots, and another rotating spot in one cell discharge successively. Based on this discharging sequence, forces exerted on a rotating spot are analyzed at different discharging stages in a half voltage cycle. A resultant force on a rotating spot with both magnitude and direction varied leads to the stochastic rotation.