The periodic rotary motion of spherical sub-millimeter-sized plastic objects is generated under a direct-current electric field in an oil phase containing a small amount of anionic or cationic surfactant. Twin-rotary motion is observed between a pair of counter-electrodes; i.e., two vortices are generated simultaneously, where the line between the centers of rotation lies perpendicular to the line between the tips of the electrodes. Interestingly, this twin rotational motion switches to the reverse direction when an anionic surfactant is replaced by a cationic surfactant. We discuss the mechanism of this self-rotary motion in terms of convective motion in the oil phase where nanometer-sized inverted micelles exist. The reversal of the direction of rotation between anionic and cationic surfactants is attributable to the difference in the charge sign of inverted micelles with surfactants. We show that the essential features in the experimental trends can be reproduced through a simple theoretical model, which supports the validity of the above mechanism.