We describe a novel rotating trait of induced-charge electroosmotic slip above a planar metal surface, a phenomenon termed "Rotating induced-charge electro-osmosis" (ROT-ICEO), in the context of a new microfluidic technology for tunable particle rotation or rotational trap. ROT-ICEO has a dynamic flow stagnation line (FSL) that rotates synchronously with a background circularly polarized electric field. We reveal that the rotating FSL of ROT-ICEO gives rise to a net hydrodynamic torque that is responsible for rotating fluids or particles in the direction of the applied rotating electric field either synchronously or asynchronously, the magnitude of which is adjusted by a balance between rotation of FSL and amplitude of angular-direction flow component oscillating at twice the field frequency. Supported by experimental observation, our physical demonstration with ROT-ICEO proves invaluable for the design of flexible electrokinetic framework in modern microfluidic system.