In a recent experiment, Schmiegelow et al. [Nat. Commun. 7, 12998 (2016)] investigated the magnetic sublevel population of Ca + ions in a Laguerre-Gaussian light beam if the target atoms were just centered along the beam axis. They demonstrated in this experiment that the sublevel population of the excited atoms is uniquely defined by the projection of the orbital angular momentum of the incident light. However, little attention has been paid so far to the question of how the magnetic sublevels are populated when atoms are displaced from the beam axis by some impact parameter b. Here, we analyze this sublevel population for different atomic impact parameters in first-order perturbation theory and by making use of the density-matrix formalism. Detailed calculations are performed especially for the 4s 2 S 1/2 → 3d 2 D 5/2 transition in Ca + ions and for the vector potential of a Laguerre-Gaussian beam in Coulomb gauge. It is shown that the magnetic sublevel population of the excited 2 D 5/2 level varies significantly with the impact parameter and is sensitive to the polarization, the radial index, as well as the orbital angular momentum of the incident light beam.