  Rebirth of X-ray polarimetric instruments will have a significant impact on
our knowledge of compact accreting sources. The properties of inner-accreting
regions of active galactic nuclei (AGNs) or X-ray binary systems (XRBs), such
as black-hole spin, their disc inclination and orientation, shape and size of
their corona, can be polarimetrically studied, parallelly to the well-known
X-ray spectroscopic and timing techniques. In this work, we provide a new
spectropolarimetric numerical estimate of X-rays in the lamp-post coronal model
for a distant observer, including a polarized reflected radiation from the
accretion disc. The local disc reflection was simulated using the codes TITAN
and STOKES and includes variable disc ionization as well as Monte Carlo
treatment of Compton multiple scatterings. We introduce a relativistic code
KYNSTOKES based on our well-tested KY package that accounts for all
relativistic effects on radiation near a black hole, apart from the returning
radiation, and adds a possibility of polarized coronal emission. We study the
spectrum, polarization degree and polarization angle at spatial infinity for
various global system parameters and we demonstrate the difference at infinity,
if analytical local reflection computations are used. We newly predict that in
the hard X-rays the reflected component can be 25% polarized and the total
emission can be 9% polarized in the most favourable, yet realistic
configurations of radio-quiet AGNs. Thus, the relativistic disc reflection
remains important for the interpretation of X-ray polarimetric observations.
