A four-dimensional intermolecular torsional potential energy surface was calculated for the cyclic homodromic water tetramer at the level of second-order Moller-Plesset perturbation theory, using a large basis set (82 basis functions per monomer). The four torsional angles omega(i) (i=1-4), which describe the positions of the "free" O-H bonds relative to the planar hydrogen-bonded O ... O ... O ... O framework were varied, while all other internal coordinates were held fixed. Ab initio calculations were performed at 307 points in the asymmetric unit of the torsional space. The points were fitted using the same seven-parameter analytical potential function as previously employed for the torsional surface of the water trimer [Burgi ed al., J. Chem. Phys. 103; 1077 (1995)]. Fits were performed for four interaction energy ranges spanning 1100, 1500, 3500 and 11 500 cm(-1) relative to the global minimum; respectively. A number of important stationary points were studied in greater detail and geometry optimized using larger basis sets at the MP2 level. Torsional interconversion pathways are mapped in terms of isopotential surface representations and contour plots. This accurate and rapidly computable potential can be employed to calculate the coupled anharmonic torsional level energies, wave functions and associated molecular properties, presented in the following paper [D. Sabo et al., J. Chem. Phys. 109, 5404 (1998)].