We presented the first three-dimensional (3D) ab initio intermolecular potential energy surface (PES) for the H3O+-Ar complex. The electronic structure computations were carried out at the explicitly correlated coupled cluster theory-F12 with an augmented correlation-consistent triple zeta basis set. Analytic 3D PES was obtained by least-squares fitting the multi-dimensional Morse/Long-Range (mdMLR) potential model to interaction energies, where the mdMLR function form was applied to the nonlinear ion-atom case for the first time. The 3D PES fitting to 1708 points has root-mean-square deviations of 0.19 cm-1 with only 108 parameters for interaction energies less than 500 cm-1. With the 3D PES of the H3O+-Ar complex, we employed the combined radial discrete variable representation/angular finite basis representation method and Lanczos algorithm to calculate rovibrational energy levels. The rotational profiles of the O-H anti-stretching vibrational bands of v3+(S)←0+ and v3-(A)←0- for the H3O+-Ar complex were predicted and were in good agreement with the experimental results.