  X-ray polarimetric missions planned for this decade will significantly
enhance our knowledge of compact accreting sources. Observations of the X-ray
polarization signal from active galactic nuclei (AGNs) or X-ray binary systems
(XRBs) will bring new means to study inner accretion flow in these objects
that, together with currently used spectroscopic and timing techniques, will
help us to determine better their properties, such as their inclination,
orientation, shape, and size of their corona as well as the black hole spin. In
this work, we present a yet missing piece in the global polarization models of
black hole accretion discs. We compute the reflected X-ray emission from the
disc in a local co-moving frame using (1) the radiative transfer code TITAN to
obtain the ionization structure of the disc and (2) the Monte Carlo code STOKES
that incorporates the physics of absorption, re-emission, and Compton
scattering to produce a complete spectropolarimetric output. We present the
final Stokes parameters I, Q, and U for a set of photon-indices of the incident
primary power-law radiation, the disc ionization parameters, incident and
emission angles, for three independent polarization states of the incident
coronal X-ray photons with a sufficient resolution in energy to allow for sharp
discussion of spectral and polarization properties. We show that the spectral
component matches well literature predictions. The polarization degree and
angle are in agreement with analytical approximations previously appearing in
reflection models and we demonstrate that the polarized reflected X-ray
emission can be, locally, quite large in the 2-12 keV band.
