  Variable active galactic nuclei showing periodic light curves have been
proposed as massive black hole binary (MBHB) candidates. In such scenarios the
periodicity can be due to relativistic Doppler-boosting of the emitted light.
This hypothesis can be tested through the timing of scattered polarized light.
Following the results of polarization studies in type I nuclei and of dynamical
studies of MBHBs with circumbinary discs, we assume a coplanar equatorial
scattering ring, whose elements contribute differently to the total polarized
flux, due to different scattering angles, levels of Doppler boost, and
line-of-sight time delays. We find that in the presence of a MBHB, both the
degree of polarization and the polarization angle have periodic modulations.
The minimum of the polarization degree approximately coincides with the peak of
the light curve, regardless of the scattering ring size. The polarization angle
oscillates around the semi-minor axis of the projected MBHB orbital ellipse,
with a frequency equal either to the binary's orbital frequency (for large
scattering screen radii), or twice this value (for smaller scattering
structures). These distinctive features can be used to probe the nature of
periodic MBHB candidates and to compile catalogs of the most promising sub-pc
MBHBs. The identification of such polarization features in gravitational-wave
detected MBHBs would enormously increase the amount of physical information
about the sources, allowing the measurement of the individual masses of the
binary components, and the orientation of the line of nodes on the sky, even
for monochromatic gravitational wave signals.
