Ionization of polarized states of Ar and Xe atoms by femtosecond probe pulse in a supersonic beam in the presence of magnetic field was studied theoretically and experimentally. The revealed oscillation structure in the photoionization signals occurs due to the Larmor precession of exited atomic states in a magnetic field. We derived analytical formulas for the photoelectron current and explained the detected oscillations in terms of photon and atomic polarization moments. Our results indicate the possibility of implementing Doppler-free spectroscopy involving bound-free transitions.