  It has long been recognised that quasi-periodic oscillations (QPOs) in the
X-ray light curves of accreting black hole and neutron star binaries have the
potential to be powerful diagnostics of strong field gravity. However, this
potential cannot be fulfilled without a working theoretical model, which has
remained elusive. Perhaps the most promising model associates the QPO with
Lense-Thirring precession of the inner accretion flow, with the changes in
viewing angle and Doppler boosting modulating the flux over the course of a
precession cycle. Here, we consider the polarization signature of a precessing
inner accretion flow. We use simple assumptions about the Comptonization
process generating the emitted spectrum and take all relativistic effects into
account, parallel transporting polarization vectors towards the observer along
null geodesics in the Kerr metric. We find that both the degree of linear
polarization and the polarization angle should be modulated on the QPO
frequency. We calculate the predicted absolute rms variability amplitude of the
polarization degree and angle for a specific model geometry. We find that it
should be possible to detect these modulations for a reasonable fraction of
parameter space with a future X-ray polarimeter such as NASA's Polarization
Spectroscopic Telescope Array (PolSTAR: the satellite incarnation of the recent
balloon experiment X-Calibur).
