Three paramagnetic defects were revealed in amorphous hydrogenated carbon-rich silicon-carbon alloy films (a-SiC:H), which were attributed to the to silicon (Si) dangling bonds (Si DB), carbon-related defects (CRD), and bulk Si DB defect bonded with nitrogen atoms Si-N2Si. The effect of thermal annealing on a-SiC:H films was studied. It was established that annealing at high temperatures leads to formation of graphite-like carbon clusters in a-SiC:H films and strong increase of the concentration of CRD, while EPR signal from Si DB disappeared. A dependence of the resonance positions for both Si DB and CRD signals on the orientation of the magnetic field relative to the a-SiC:H film plane was found at Q-band and D-band frequencies and was explained by the influence of demagnetizing fields, which is becoming significant at high spin density of the paramagnetic centers, higher microwave frequency, and low temperature. A demagnetizing field of 11 Gs was found in annealed a-SiC:H film at 140 GHz and 4.2 K.