Aims:The nature of S Ori 70 (S Ori J053810.1-023626), a faint mid-T type object found towards the direction of the young σ Orionis cluster, is still under debate. We intend to find out whether it is a field brown dwarf or a 3-Myr old planetary-mass member of the cluster. Methods: We report on near-infrared {JHK}s and mid-infrared [3.6] and [4.5] IRAC/Spitzer photometry recently obtained for S Ori 70. The new near-infrared images (taken 3.82 yr after the discovery data) allowed us to derive the first proper motion measurement for this object. Results: The colors (H-K_s), (J-K_s) and Ks - [3.6] appear discrepant when compared to T4-T7 dwarfs in the field. This behavior could be ascribed either to a low-gravity atmosphere or to an atmosphere with a metallicity that is significantly different than solar. The small proper motion of S Ori 70 (11.0 ± 5.9 mas yr-1) indicates that this object is farther away than expected if it were a single field T dwarf lying in the foreground of the σ Orionis cluster. Our measurement is consistent with the proper motion of the cluster within 1.5σ the astrometric uncertainty. Conclusions: Taking into account both S Ori 70's proper motion and the new near- and mid-infrared colors, a low-gravity atmosphere remains as the most likely explanation for our observations. This supports S Ori 70's membership in σ Orionis, with an estimated mass in the interval 2-7 M_Jup, in agreement with our previous derivation.