  X-ray astronomy allows study of objects which may be associated with compact
objects, i.e. neutron stars or black holes, and also may contain strong
magnetic fields. Such objects are categorically non-spherical, and likely
non-circular when projected on the sky. Polarization allows study of such
geometric effects, and X-ray polarimetry is likely to become feasible for a
significant number of sources in the future. Potential targets for future X-ray
polarization observations are the high-mass X-ray binaries (HMXBs), which
consist of a compact object in orbit with an early type star. In this paper ws
show that X-ray polarization from HMXBs has a distinct signature which depends
on the source inclination and orbital phase. The presence of the X-ray source
displaced from the star creates linear polarization even if the primary wind is
spherically symmetric whenever the system is viewed away from conjunction.
Direct X-rays dilute this polarization whenever the X-ray source is not
eclipsed; at mid-eclipse the net polarization is expected to be small or zero
if the wind is circularly symmetric around the line of centers. Resonance line
scattering increases the scattering fraction, often by large factors, over the
energy band spanned by resonance lines. Real winds are not expected to be
spherically symmetric, or circularly symmetric around the line of centers,
owing to the combined effects of the compact object gravity and ionization on
the wind hydrodynamics. A sample calculation shows that this creates
polarization fractions ranging up to tens of percent at mid-eclipse.
