Context. The size and geometry of the broad-line region (BLR) in active galactic nuclei (AGNs) are among the main ingredients in determining the mass of the accreting black hole. Size and geometry can be constrained by determining the delay between the optical continuum and the flux reprocessed by the BLR, in particular, through the emission lines.Aims. We propose here that the delay between polarized and unpolarized light can also be used in much the same way to constrain the size of the BLR; we verify that meaningful results can be expected from observations using this technique.Methods. We used our code STOKES to simulate polarized radiative transfer. We determined the response of the environment of the central source (BLR, dust torus, and polar wind) to randomly generated fluctuations in the central source. We then calculated the cross correlation between the simulated polarized flux and the total flux to estimate the time delay that would be provided by observations using the same method.Results. The BLR is the main contributor to the delay between the polarized flux and the total flux. This delay is independent of the observation wavelength.Conclusions. This validates the use of polarized radiation in the optical/UV band to estimate the geometrical properties of the BLR in type I AGNs, in which the viewing angle is close to pole-on and the BLR is not obscured by the dust torus.