Ionization of three-photon excited polarized states of argon atoms by circularly polarized probe light was studied in a supersonic beam. The revealed oscillation structure in the observed photoionization signals due to the Larmor precession of excited atomic states in a magnetic field allowed finding novel data for the Landé g-factors. We derived analytical formulas for the photoelectron current and explained the various types of the detected oscillations in terms of the principal lines among multiplet components of optical transitions. Our results indicate the possibility of implementing Doppler-free spectroscopy involving bound-free transitions.