  The effect of gravitational Faraday rotation was predicted in the 1950s, but
there is currently no practical method for measuring this effect. Measuring
this effect is important because it will provide new evidence for correctness
of general relativity, in particular, in the strong field limit. We predict
that the observed degree and angle of the X-ray polarization of a
cosmologically distant quasar microlensed by the random star field in a
foreground galaxy or cluster lens vary rapidly and concurrently with flux
during caustic-crossing events using the first simulation of quasar X-ray
microlensing polarization light curves. Therefore, it is possible to detect
gravitational Faraday rotation by monitoring the X-ray polarization of
gravitationally microlensed quasars. Detecting this effect will also confirm
the strong gravity nature of quasar X-ray emission.
