We show that the Poynting-Robertson drag on electrons in an optically thin accretion flow around active gravitating objects generates strong azimuthal electric currents that give rise to astrophysically significant magnetic fields. The mechanism is most effective in accretion disks around stellar size black holes, where the characteristic time for building-up equipartition magnetic fields is of the order of a few hours. We support our physical picture with numerical MHD simulations showing continuous magnetic field growth in an initially unmagnetized disk model .