  We present new calculations of X-ray polarization from accreting black holes
(BHs), using a Monte-Carlo ray-tracing code in full general relativity. In our
model, an optically thick disk in the BH equatorial plane produces thermal seed
photons with polarization oriented parallel to the disk surface. These seed
photons are then inverse-Compton scattered through a hot (but thermal) corona,
producing a hard X-ray power-law spectrum. We consider three different models
for the corona geometry: a wedge ``sandwich'' with aspect ratio H/R and
vertically-integrated optical depth tau_0 constant throughout the disk; an
inhomogeneous ``clumpy'' corona with a finite number of hot clouds distributed
randomly above the disk within a wedge geometry; and a spherical corona of
uniform density, centered on the BH and surrounded by a truncated thermal disk
with inner radius R_edge. In all cases we find a characteristic transition from
horizontal polarization at low energies to vertical polarization above the
thermal peak; the vertical direction is defined as the projection of the BH
spin axis on the plane of the sky. We show how the details of the
spectropolarization signal can be used to distinguish between these models and
infer various properties of the corona and BH. Although the bulk of this paper
focuses on stellar-mass BHs, we also consider the effects of coronal scattering
on the X-ray polarization signal from supermassive BHs in active galactic
nuclei.
