  Recent X-ray polarimetric data on the prototypical black hole X-ray binary
Cyg~X-1 from the Imaging X-ray Polarimetry Explorer present tight constraints
on accretion geometry in the hard spectral state. Contrary to general
expectations of a low, <1% polarization degree (PD), the observed average PD
was found to be a factor of 4 higher. Aligned with the jet position angle on
the sky, the observed polarization favors geometry of the X-ray emission region
stretched normally to the jet in the accretion disk plane. The high PD is,
however, difficult to reconcile with the low orbital inclination of the binary
$i\approx30$ deg. We suggest that this puzzle can be explained if the emitting
plasma is outflowing with a mildly relativistic velocity $\gtrsim0.4\,c$. Our
radiative transfer simulations show that Comptonization in the outflowing
medium elongated in the plane of the disk radiates X-rays with the degree and
direction of polarization consistent with observations at $i\approx30$ deg.
