  Measurements of the angular momentum (spin) of astrophysical black holes are
extremely important, as they provide information on the black hole formation
and evolution. We present simulated observations of a X-ray binary system with
the Imaging X-ray Polarimetry Explorer (IXPE), with the aim to study the
robustness of black hole spin and geometry measurements using X-ray
polarimetry. As a representative example, we used the parameters of GRS
1915+105 in its former unobscured, soft state. In order to simulate the
polarization properties, we modeled the source emission with a multicolor
blackbody accounting for thermal radiation from the accretion disk, including
returning radiation. Our analysis shows that the polarimetric observations in
the X-ray waveband will be able to estimate both spin and inclination of the
system with a good precision (without returning radiation we obtained for the
lowest spin $\Delta a \leq 0.4$ (0.4/0.998 $\sim$ 40%) for spin and $\Delta i
\leq 30^\circ$ (30$^\circ$/70$^\circ$ $\sim$ 43%) for inclination, while for
the higher spin values we obtained $\Delta a \leq 0.12$ ($\sim$ 12%) for spin
and $\Delta i \leq 20^\circ$ ($ \sim $ 29%) for inclination, within 1$ \sigma $
errors). When focusing on the case of returning radiation and treating
inclination as a known parameter, we were able to successfully reconstruct spin
and disk albedo in $\Delta a \leq 0.15$ ($\sim$ 15%) interval and $\Delta$
albedo $\leq 0.45$ (45%) intervals within 1$ \sigma $ errors. We conclude that
X-ray polarimetry will be a useful tool to constrain black hole spins, in
addition to timing and spectral-fitting methods.
