Pure rotational spectra have been calculated for the three isotopomers of the Cl-2-Ar van der Waals complex formed by Cl-2 in its ground electronic state. The potential energy surface involved is a sum of pairwise. Morse atom-atom interactions, which are merged asymptotically into an anisotropic van der Waals form. The Morse atom-atom interactions have been refined by adjusting their parameters to obtain agreement with both excitation spectra and recent microwave transitions observed for the Cl-35(2)-Ar van der Waals complex, whereas the anisotropic long-range part of the potential surface has been taken from ab initio results [Mol. Phys. 80, 533 (1993)]. The present model potential surface predicts a T-shaped structure for the complex, in agreement with experiment. Excellent agreement has been found between the calculated and experimental microwave transition frequencies for the (ClCl)-Cl-35-Cl-37-Ar complex. Good agreement has also been found between the experimentally determined bond energy, bond length, and average "bond angle" governing the overall geometry of the complex and the corresponding quantities determined from dynamical calculations based upon the present potential surface. The new potential surface has also been utilized to predict the microwave spectrum of the Cl-37(2)-Ar isotopomer.