ABSTRACT 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 an 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 modelled the source emission with a multicolour blackbody accounting for thermal radiation from the accretion disc, 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 Δa ≤ 0.4 (0.4/0.998 ∼ 40 per cent) for spin and Δi ≤ 30° (30°/70$^∘ \, ∼$ 43 per cent) for inclination, while for the higher spin values we obtained Δa ≤ 0.12 (∼12 per cent) for spin and Δi ≤ 20° (∼29 per cent) for inclination, within 1σ errors]. When focusing on the case of returning radiation and treating inclination as a known parameter, we were able to successfully reconstruct spin and disc albedo in Δa ≤ 0.15 (∼15 per cent) interval and Δ albedo ≤0.45 (45 per cent) intervals within 1σ 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.