An argon-argon interatomic potential energy curve was derived from quantum-mechanical ab initio calculations using basis sets of up to d-aug-cc-pV(6+d)Z quality supplemented with bond functions and ab initio methods up to CCSDT(Q). In addition, corrections for relativistic effects were determined. An analytical potential function was fitted to the ab initio values and utilised to compute the rovibrational spectrum. The quality of the interatomic potential function was tested by comparison of the calculated spectrum with experimental ones and those derived from other potentials of the literature. In a following paper the new interatomic potential is used to determine selected thermophysical properties of argon by means of quantum-statistical mechanics and the corresponding kinetic theory considering two-body and three-body interactions.