The influence of the ocean depth and anisotropic tilt angle on vertical underwater wireless optical communication (UWOC) systems is considered in this study. We propose a power spectrum model of oceanic turbulence with an anisotropic tilt angle for the first time. Thereafter, the expression of the scintillation index is derived for a spherical wave propagating over anisotropic oceanic turbulence in the vertical link. In addition, considering the temperature and salinity, relevant data of the Atlantic and Pacific oceans at different depths are selected to study further the effect of ocean depth on the scintillation index. The results indicate that the scintillation index strongly depends on the ocean depth and anisotropic tilt angle. Moreover, the scintillation index is also related to other parameters, such as temperature and salinity, kinematic viscosity, the anisotropic factor, optical wavelength, and propagation distance. The presented results can be beneficial in designing optical wireless communication systems in the ocean environment.