Spin parameters of stellar-mass black holes in X-ray binaries are currently being estimated by fitting the X-ray continuum spectra of their accretion disk emission. For this method, it is necessary to know the inclination of the X-ray-producing inner region of the disk. Since the inner disk is expected to be oriented perpendicular to the spin axis of the hole, the usual practice is to assume that the black hole spin is aligned with the orbital angular momentum vector of the binary, and to estimate the inclination of the latter from ellipsoidal modulations in the light curve of the secondary star. We show that the inclination of the disk can be inferred directly if we have both spectral and polarization information on the disk radiation. The predicted degree of polarization varies from 0% to 5% as the disk inclination changes from face-on to edge-on. With current X-ray polarimetric techniques the polarization degree of a typical bright X-ray binary could be measured to an accuracy of 0.1% by observing the source for about 10 days. Such a measurement would constrain the disk inclination to within a degree or two and would significantly improve the reliability of black hole spin estimates. In addition, it would provide new information on the tilt between the black hole spin axis and the orbital rotation axis of the binary, which would constrain any velocity kicks experienced by stellar-mass black holes during their formation.
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