A complex of argon with silver iodide (Ar⋯Ag−I) has been formed in the gas phase by laser ablation of a silver iodide rod in the presence of a pulse of argon gas and its ground-state rotational spectrum has been detected by means of a chirped-pulse, F-T microwave instrument. Ar⋯Ag−I was characterised both by experimental properties determined from its rotational spectrum and by ab initio calculations carried out at the CCSD(T)(F12c)/cc-pVTZ-F12 explicitly correlated level of theory. The molecule was shown to be linear in the ground state, with atoms in the order shown. The Ar⋯Ag and Ag–I bond lengths r0(Ar⋯Ag) = 2.6759 Å and r0(Ag--I) = 2.5356 Å, the dissociation energy De = 16.7 kJ mol-1 for the process Ar⋯Ag−I = Ar + Ag−I, the intermolecular quadratic stretching force constant FAr⋯Ag = F22 = 20.2 N m -1 and the increase 0.033 in the ionicity ic of Ag–I when it enters the complex are reported. The opportunity has been taken to compare the way in which these properties vary along the series Ar⋯Ag−X (X = F, Cl, Br and I).