  The high-energy emission ($400$ keV $- 2$ MeV) of Cygnus X-1 --the most
well-studied Galactic black hole-- was recently found to be strongly polarized.
The origin of this radiation is still unknown. In this work, we suggest that it
is the result of non-thermal processes in the hot corona around the accreting
compact object, and study the polarization of high-energy radiation expected
for black hole binaries. Two contributions to the total magnetic field are
taken into account in our study, a small scale random component related to the
corona, and an ordered magnetic field associated with the accretion disk. The
degree of polarization of gamma-ray emission for this particular geometry is
estimated, as well as the angle of the polarization vector. We obtain that the
corona+disk configuration studied in this work can account for the high degree
of polarization of gamma-rays detected in galactic black holes without the need
of a relativistic jet; specific predictions are made for sources in a low-hard
state. In particular, the model is applied to the transient source \xtee; we
show that if a new outburst of \xte is observed, then its gamma-ray
polarization should be measurable by future instruments, such as ASTRO-H or the
proposed ASTROGAM.
