The ground state Ar-C-2 potential energy surface has been calculated ab initio and fitted by means of an effective ArC pair interaction model. The global minimum of energy is predicted to occur for the linear Ar-C-2 geometry, while a saddle point is predicted for the T-shaped geometry. This behaviour is distinct from that found for rare gas complexes with heavier symmetric diatomic molecules of the second row atoms. The results are analysed in terms of effective ArC potentials, which are perturbed by intramolecular forces in C-2, and differ considerably from the Lennard-Jones potentials normally used to model these interactions. The present model is applied to small ArnC2 (n=2-4) clusters and used to predict the microwave spectrum of ArC2.