X-ray polarization measurement is a unique tool which may provide crucial information regarding the emission mechanism and the geometry of various astrophysical sources, such as neutron stars, accreting black holes, pulsar wind nebulae, active galactic nuclei, supernova remnants etc., and can help us to probe matter under extreme magnetic fields and extreme gravitational fields. Although the three other domains of X-ray astronomy, i.e. timing, spectral and imaging are well developed, there has been very little progress in X-ray polarimetry with only one definitive polarization measurement and a few upper limits available so far. Radiation from accreting black holes in their thermal-dominated (high soft) state is expected to be polarized due to scattering in the plane-parallel atmosphere of the disc. Furthermore, special and general relativistic effects in the innermost parts of the disc predict energy-dependent rotation in the plane of polarization and some distinct signatures which can be used as a probe for measuring the parameters of the black hole, like its spin, emissivity profile and the angle of inclination of the system. We present the results from an analysis of expected minimum detectable polarization from some of the galactic black hole binaries, GRO J1655−40, GX 339−4, H1743−322, Cygnus X-1 and XTE J1817−330, in their thermal-dominated state with a proposed Thomson X-ray polarimeter. A proposal for a scattering polarimeter has been submitted to the Indian Space Research Organization for a dedicated small satellite mission and a laboratory unit has been built. Along with the measurement of the degree of polarization, the polarization angle measurement is also important, hence the error in the polarization angle measurement for a range of detection significance is also obtained.