Several dynamical processes may induce considerable electric currents in the atmospheres of magnetic chemically peculiar (CP) stars. The Lorentz force, which results from the interaction between the magnetic field and the induced currents, modifies the atmospheric structure and induces the characteristic rotational variability in the hydrogen Balmer lines. To study this phenomena we have initiated a systematic spectroscopic survey of the Balmer lines variation in magnetic CP stars. In this paper we continue presenting the results of the program, focusing on the high-resolution spectral observations of the A0p star θ Aur (HD 40312). We detected a significant variability in the Hα, Hβ, and Hγ spectral lines during the full rotation cycle of the star. This variability is interpreted in the framework of the model atmosphere analysis, which accounts for the Lorentz force effects. Both the inward- and outward-directed Lorentz forces are considered under the assumption of the axisymmetric dipole or dipole+quadrupole magnetic field configurations. We demonstrate that only the model with the outwardly directed Lorentz force in the dipole+quadrupole configuration is able to reproduce the observed hydrogen-line variation. These results present new strong evidence of non-zero global electric currents in the atmosphere of an early-type magnetic star.