  Relativistic magnetic reconnection is a potential particle acceleration
mechanism for high-frequency BL Lacs (HBLs). The {\it Imaging X-ray Polarimetry
Explorer} ({\it IXPE}) scheduled to launch in 2021 has the capability to probe
the magnetic field evolution in HBLs, examining the magnetic reconnection
scenario for the HBL flares. In this paper, we make the first attempt to
self-consistently predict HBL X-ray polarization signatures arising from
relativistic magnetic reconnection via combined particle-in-cell (PIC) and
polarized radiation transfer simulations. We find that although the intrinsic
optical and X-ray polarization degrees are similar on average, the X-ray
polarization is much more variable in both polarization degree and angle (PD
and PA). Given the sensitivity of the {\it IXPE}, it may obtain one to a few
polarization data points for one flaring event of nearby bright HBLs Mrk~421
and 501. However, it may not fully resolve the highly variable X-ray
polarization. Due to the temporal depolarization, where the integration of
photons with variable polarization states over a finite period of time can
lower the detected PD, the measured X-ray PD can be considerably lower than the
optical counterpart or even undetectable. The lower X-ray PD than the optical
thus can be a characteristic signature of relativistic magnetic reconnection.
For very bright flares where the X-ray polarization is well resolved,
relativistic magnetic reconnection predicts smooth X-ray PA swings, which
originate from large plasmoid mergers in the reconnection region.
