The influence of the intrinsic spin of electrons on the propagation of circularly polarized waves in a magnetized plasma is considered. New eigenmodes are identified, one of which propagates below the electron cyclotron frequency, one above the spin-precession frequency, and another close to the spin-precession frequency. The latter corresponds to the spin modes in ferromagnets under certain conditions. In the non-relativistic motion of electrons, the spin effects become noticeable even when the external magnetic field B-0 is below the quantum critical magnetic field strength, i.e. B-0 < B-Q = 4.4138x10(9) T and the electron density satisfies n(0) >> n(c) similar or equal to 10(32) m(-3). The importance of electron spin (paramagnetic) resonance (ESR) for plasma diagnostics is discussed.