The rotational spectra of the complexes Ar-CuF, Ar-CuCl, and Ar-CuBr have been observed in the frequency range 5-22 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-Cu stretching frequency estimated as similar to 200 cm(-1). Isotopic data have been used to calculate an r(0) structure for Ar-CuF, while for Ar-CuCl and Ar-CuBr partial substitution structures have also been obtained. To reduce zero-point vibrational effects a double substitution method (r(d)) has also been employed to calculate the structures of Ar-CuCl and Ar-CuBr. The Ar-Cu distance has been found to be rather short and to range from 2.22 Angstrom in Ar-CuF to 2.30 Angstrom in Ar-CuBr. Ab initio calculations at the MP2 level of theory model the geometries and stretching frequencies well and predict an Ar-Cu bond energy in Ar-CuF of similar to 47.3 kJ mol(-1). Large changes in the Cu nuclear quadrupole coupling constant on complex formation show that extensive charge rearrangement occurs upon formation of the complexes. This, in conjunction with the sizable dissociation energy, suggests that the Ar-Cu bonds in these complexes are weakly covalent. The rotational spectrum of CuF has also been reinvestigated to improve the hyperfine constants.