The rotational spectra of the complexes Ar-AgF, Ar-AgCl, and Ar-AgBr have been observed in the frequency range 6-20 GHz using a pulsed jet cavity Fourier transform microwave spectrometer. All the complexes are linear and rather rigid in the ground vibrational state, with the Ar-Ag stretching frequency estimated as similar to 140 cm(-1). Isotopic data have been used to calculate an r(0) structure for Ar-AgF, while for Ar-AgCl and Ar-AgBr partial substitution structures have also been obtained. To reduce zero-point vibrational effects a double substitution method (r(d)) was employed to calculate the structures of Ar-AgCl and Ar-AgBr. The Ar-Ag bond distance has been found to be rather short and to range from 2.56 Angstrom in Ar-AgF to 2.64 Angstrom in Ar-AgBr. Ab initio MP2 and density functional theory calculations for Ar-AgF and Ar-AgCl model the geometries and stretching frequency well, and predict an Ar-Ag bond energy in Ar-AgF of similar to 23 kJ mol(-1). These results indicate that the Ar-AgX complexes are more strongly bound than typical van der Waals complexes. Analysis of the halogen nuclear quadrupole coupling constants was unable to confirm whether extensive electron rearrangement occurs upon formation of the complexes.