A rotary wrapping machine (30, 110) for packaging products by means of a film unwound from a reel comprises a frame (13, 113) carrying a dispensing unit (19, 119) which is electrically controlled to dispense the packaging film from a reel of film present in the dispensing unit (19, 119). The dispensing unit is supported on the frame so as to be driven rotationally along a closed path around a packaging zone (38, 138) which contains a product to be wrapped with the film. Along the closed path there is a power supply antenna (25, 125) which is connected to an antenna power supply unit (26, 126) for transferring, by means of electrical induction, electric power to a corresponding receiver (28, 128) which is movable along the antenna together with the said dispensing unit and which supplies in turn electric power to the dispensing unit.