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• . We detect two shifted Fe lines, in several observations, as predicted in our numerical simulations of caustic crossings. The current ∆E-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.