  We present a promising new technique, the g-distribution method, for
measuring the inclination angle (i), the innermost stable circular orbit
(ISCO), and the spin of a supermassive black hole. The g-distribution method
uses measurements of the energy shifts in the relativistic iron line emitted by
the accretion disk of a supermassive black hole due to microlensing by stars in
a foreground galaxy relative to the g-distribution shifts predicted from
microlensing caustic calculations. We apply the method to the gravitationally
lensed quasars RX J1131-1231 (z_s=0.658, z_l=0.295), QJ 0158-4325 (z_s=1.294,
z_l=0.317), and SDSS 1004+4112 (z_s=1.734, z_l=0.68). For RX J1131-1231 our
initial results indicate that r_ISCO<8.5 gravitational radii (r_g) and i > 76
degrees. We detect two shifted Fe lines, in several observations, as predicted
in our numerical simulations of caustic crossings. The current
DeltaE-distribution of RX J1131-1231 is sparsely sampled but further X-ray
monitoring of RX J1131-1231 and other lensed quasars will provide improved
constraints on the inclination angles, ISCO radii and spins of the black holes
of distant quasars.
