Based on spectropolarimetry for a number of active galactic nuclei in Seyfert 1 type galaxies observed with the 6-m BTA telescope, we have estimated the spins of the supermassive black holes at the centers of these galaxies. We have determined the spins based on the standard Shakura-Sunyaev accretion disk model. More than 70% of the investigated active galactic nuclei are shown to have Kerr supermassive black holes with a dimensionless spin greater than 0.9.