  Propagation of light in the gravitational field of self-gravitating spinning
bodies moving with arbitrary velocities is discussed. The gravitational field
is assumed to be "weak" everywhere. Equations of motion of a light ray are
solved in the first post-Minkowskian approximation that is linear with respect
to the universal gravitational constant $G$. We do not restrict ourselves with
the approximation of gravitational lens so that the solution of light geodesics
is applicable for arbitrary locations of source of light and observer. This
formalism is applied for studying corrections to the Shapiro time delay in
binary pulsars caused by the rotation of pulsar and its companion. We also
derive the correction to the light deflection angle caused by rotation of
gravitating bodies in the solar system (Sun, planets) or a gravitational lens.
The gravitational shift of frequency due to the combined translational and
rotational motions of light-ray-deflecting bodies is analyzed as well. We give
a general derivation of the formula describing the relativistic rotation of the
plane of polarization of electromagnetic waves (Skrotskii effect). This formula
is valid for arbitrary translational and rotational motion of gravitating
bodies and greatly extends the results of previous researchers. Finally, we
discuss the Skrotskii effect for gravitational waves emitted by localized
sources such as a binary system. The theoretical results of this paper can be
applied for studying various relativistic effects in microarcsecond space
astrometry and developing corresponding algorithms for data processing in space
astrometric missions such as FAME, SIM, and GAIA.
