We discuss the role of pairing anti-halo effect in the observed odd-even staggering in reaction cross sections for 30,31,32 Ne and 36,37,38 Mg isotopes by taking into account the ground state deformation of these nuclei. To this end, we construct the ground state density for the 30,31 Ne and 36,37 Mg nuclei based on a deformed Woods-Saxon potential, while for the 32 Ne and 38 Mg nuclei we also take into account the pairing correlation using the Hartree-Fock-Bogoliubov method. We demonstrate that, when the one-neutron separation energy is small for the odd-mass nuclei, a significant odd-even staggering still appears even with finite deformation, although the degree of staggering is somewhat reduced compared to the spherical case. This implies that the pairing anti-halo effect in general plays an important role in generating the odd-even staggering in reaction cross sections for weakly bound nuclei.