Xenon ion velocity is mapped in the magnetic nozzle of a circular waveguide electron cyclotron resonance thruster operating at 5.8 GHz by means of laser-induced fluorescence spectroscopy in the near-infrared spectral range. An array of thruster operational parameters are explored to investigate the influence on the acceleration profile and terminal ion velocity. Owing to several mechanisms which broaden the measured spectra, e.g. Paschen-Back/Zeeman effect, inference of the most probable velocity along with the axial kinetic temperature requires full lineshape modeling, especially in the near-field plume and inside the source. Ions are effectively accelerated along the magnetic nozzle, reaching up to 12000 m/s for the lowest neutral pressure tested. A relatively large axial kinetic temperature is observed, typically in the order of 5000 K, which can be attributed to an extended ionization region that overlaps with the acceleration region.