A small fraction of hot OBA stars host global magnetic fields with field strengths of the order of 0.1-10 kG. This leads to the creation of persistent surface structures (spots) in stars with sufficiently weak winds as a result of the radiative diffusion. These spots become evident in spectroscopic and photometric variability. This type of variability is not expected in stars with strong winds, where the wind inhibits the radiative diffusion. Therefore, a weak photometric variability of the magnetic Of?p star HD 191612 is attributed to the light absorption in the circumstellar clouds. We study the nature of the photometric variability of HD 191612. We assume that the variability results from variable wind blanketing induced by surface variations of the magnetic field tilt and modulated by stellar rotation. We used our global kinetic equilibrium (NLTE) wind models with radiative force determined from the radiative transfer equation in the comoving frame (CMF) to predict the stellar emergent flux. Our models describe the stellar atmosphere in a unified manner and account for the influence of the wind on the atmosphere. The models are calculated for different wind mass-loss rates to mimic the effect of magnetic field tilt on the emergent fluxes. We integrate the emergent fluxes over the visible stellar surface for individual rotational phases, and calculate the rotationally modulated light curve of HD 191612. The wind blanketing that varies across surface of HD 191612 is able to explain a part of the observed light variability in this star. The mechanism is able to operate even at relatively low mass-loss rates. The remaining variability is most likely caused by the flux absorption in circumstellar clouds. The variable wind blanketing is an additional source of the light variability in massive stars. The presence of the rotational light variability may serve as a proxy for the magnetic field.