  We study the gravitational Faraday rotation, on linearly polarized light rays
emitted by a pulsar, orbiting another compact object. We relate the rotation
angle to the orbital phase of the emitting pulsar, as well as to other
parameters describing its orbit and the orientation of the angular momentum of
the binary companion. We give numerical estimates of the effect for the
double-pulsar system PSR J0737-3039, and we note that the expected magnitude is
exceedingly small, making the effect unlikely to be observed with present
technology. It is however interesting per se, since in this phenomenon,
gravito-magnetism plays a leading role, unlike what happens, for instance, when
studying light bending or gravitational time delay, where it appears as a
correction to the gravito-electric contribution. Also, we envisage the
possibility that this effect could be relevant, at least in principle, for a
pulsar orbiting a non charged black-hole.
