  In `spider' pulsars, the X-ray band is dominated by Intrabinary Shock (IBS)
synchrotron emission. While the double-peaked X-ray light curves from these
shocks have been well characterized in several spider systems (both black
widows and redbacks), the polarization of this emission is yet to be studied.
Motivated by the new polarization capability of the Imaging X-ray Polarization
Explorer (IXPE) and the confirmation of highly ordered magnetic fields in
pulsar wind nebulae, we model the IBS polarization, employing two potential
magnetic field configurations: toroidal magnetic fields imposed by the
pre-shock pulsar wind, and tangential shock-generated fields, which follow the
post-shock flow. We find that if IBSs host ordered magnetic fields, the
synchrotron X-rays from spider binaries can display a high degree of
polarization ($\gtrsim50\%$), while the polarization angle variation provides a
good probe of the binary geometry and the magnetic field structure. Our results
encourage polarization observational studies of spider pulsars, which can
distinguish the proposed magnetic models and better constrain unique properties
of these systems.
