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

X-ray Polarization from High Mass X-ray Binaries