We report the experimental observation of the rotation of the polarization plane of light propagating in a gas of fast-spinning molecules (molecular super-rotors). In the observed effect, related to Fermis prediction of polarization drag by a rotating medium, the vector of linear polarization tilts in the direction of molecular rotation due to the rotation-induced difference in the refractive indices for the left and right circularly polarized components. We use an optical centrifuge to bring the molecules in a gas sample to ultrafast unidirectional rotation and measure the polarization drag angles of the order of 0.2 milliradians in a number of gases under ambient conditions. We demonstrate an all-optical control of the drag magnitude and direction, and investigate the robustness of the mechanical Faraday effect with respect to molecular collisions.