Thin accretion discs around massive black holes are believed to produce much of the observed optical-UV emission from AGN. Classical calculations predict that this radiation is highly polarized at large inclination angles, in contrast to observations of quasars and Seyfert galaxies. We have calculated the spectrum and polarization of such discs using an improved radiative transfer method with all the relevant opacity sources, and a full general relativistic treatment of the radiation propagation. We find the overall polarization to be much smaller than previously suggested. At low frequencies the disc opacity significantly reduces its polarization while at high frequencies general relativistic effects depolarize the radiation. The calculated degree of polarization, and its wavelength dependence, are consistent with the available observations. We predict that the degree of polarization should show a distinct broad feature near the Lyman edge, and that the polarization plane should rotate at high frequencies. The first effect will confirm the thermal nature of the observed UV radiation and the second the existence of massive black holes at the centre of AGN.