Although a cubic phase of Mn$_3$Ga with an antiferromagnetic order has been theoretically predicted, it has not been experimentally verified in a bulk or film form. Here, we report the structural, magnetic, and electrical properties of antiferromagnetic cubic Mn$_3$Ga (C-Mn$_3$Ga) thin films, in comparison with ferrimagnetic tetragonal Mn$_3$Ga (T-Mn3Ga). The structural analyses reveal that C-Mn$_3$Ga is hetero-epitaxially grown on MgO substrate with the Cu$_3$Au-type cubic structure, which transforms to T-Mn$_3$Ga as the RF sputtering power increases. The magnetic and magnetotransport data show the antiferromagnetic transition at T$_N$ = 400 K for C-Mn$_3$Ga and the ferrimagnetic transition at T$_C$ = 820 K for T-Mn$_3$Ga. Furthermore, we find that the antiferromagnetic C-Mn$_3$Ga exhibits a higher electrical resistivity than the ferrimagnetic T-Mn$_3$Ga, which can be understood by spin-dependent scattering mechanism.