We report on the measurement of the linear polarization degree of the
3s2S1/2 $\ensuremath{\rightarrow}$
3p2P3/2 $\ensuremath{\rightarrow}$
5s2S1/2 transition in atomic sodium. A linearly polarized pump laser creates an alignment in the excited
23Na
3p2P3/2 level. From the spectra, we extracted the inelastic collision cross section for the disalignment of the excited atoms by collisions with ground-level argon or xenon atoms. Measurements were done by monitoring the intensity of the cascade fluorescence from the
4p2P1/2 $\ensuremath{\rightarrow}$
3s2S1/2 transition at 330.29 nm, in the presence of Ar and Xe for pressures ranging from 5.3 to 146.6 mbar. We demonstrated that the polarization measurement can provide important information about the alignment-dependent inelastic process in alkali-metal--rare-gas collisions. A depolarization cross-section value of 196 (22) \AA{}
2 for Na-Ar and 357 (21) \AA{}
2 for Na-Xe are obtained.