Thermal emission from the accretion disc around a black hole can be polarized, due to Thomson scattering in a disc atmosphere. In Newtonian space, the polarization angle must be either parallel or perpendicular to the projection of the disc axis on the sky. As first pointed out by Stark and Connors in 1977, General Relativity effects strongly modify the polarization properties of the thermal radiation as observed at infinity. Among these effects, the rotation of the polarization angle with energy is particularly useful as a diagnostic tool. In this paper, we extend the Stark and Connors calculations by including the spectral hardening factor, several values of the optical depth of the scattering atmosphere and rendering the results to the expected performances of planned X-ray polarimeters. In particular, to assess the perspectives for the next generation of X-ray polarimeters, we consider the expected sensitivity of the detectors onboard the planned POLARIX and IXO missions. We assume the two cases of a Schwarzschild and an extreme Kerr black hole with a standard thin disc and a scattering atmosphere. We compute the expected polarization degree and the angle as functions of the energy as they could be measured for different inclinations of the observer, optical thickness of the atmosphere and different values of the black hole spin. We assume the thermal emission dominates the X-ray band. Using the flux level of the microquasar GRS 1915+105 in the thermal state, we calculate the observed polarization.
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