The Ar+ densities in the terrestrial ionosphere are computed for both low and high solar activity models. The reaction N2 +(v>0)+Ar → N2+Ar+ is found to be a significant source of Ar+, nearly equal to photoionization and electron impact ionization in the high solar activity model. Peak densities of Ar+ of 11 cm-3 near 190 km and 22 cm-3 near 220 km are predicted for the low and high solar activity models. It is suggested that a simultaneous measurement of Ar+ and Ar densities would provide a test for the presence of vibrationally excited N2 + in the terrestrial ionosphere.