  We use a ray-tracing technique to compute the observed spectrum of a thin
accretion disk around a Kerr black hole. We include all relativistic effects
such as frame-dragging, Doppler boost, gravitational redshift, and bending of
light by the gravity of the black hole. We also include self-irradiation of the
disk as a result of light deflection. Assuming that the disk emission is
locally blackbody, we show how the observed spectrum depends on the spin of the
black hole, the inclination of the disk, and the torque at the inner edge of
the disk. We find that the effect of a nonzero torque on the spectrum can, to a
good approximation, be absorbed into a zero-torque model by adjusting the mass
accretion rate and the normalization. We describe a computer model, called
KERRBB, which we have developed for fitting the spectra of black hole X-ray
binaries. Using KERRBB within the X-ray data reduction package XSPEC, and
assuming a spectral hardening factor f_col = 1.7, we analyze the spectra of
three black hole X-ray binaries: 4U1543-47, XTE J1550-564, and GRO J1655-40. We
estimate the spin parameters of the black holes in 4U1543-47 and GRO J1655-40
to be a/M ~ 0.6 and ~ 0.6-0.7, respectively. If f_col ~ 1.5-1.6, as in a recent
study, then we find a/M ~ 0.7-0.8 and ~ 0.8-0.9, respectively. These estimates
are subject to additional uncertainties in the assumed black hole masses,
distances and disk inclinations.
