The propagation model of orbital angular momentum (OAM) modes carried by the perfect vortex (pv) beam through anisotropic oceanic turbulence links is established and the factors influencing the OAM propagation are discussed. The findings show that the self-focusing property of pv beams is beneficial to the propagation of OAM modes: a smaller topological charge, a smaller initial radius, and an optimized half-ring width can alleviate degrading effects of turbulence on the pv beam. Additionally, the pv beam with a longer wavelength is more resistant to turbulent interference. The oceanic conditions with a higher dissipation rate of kinetic energy per unit mass of seawater, larger values of anisotropy and inner-scale factor, a smaller temperature-salinity contribution ratio, or a lower mean-squared temperature dissipation rate can improve the signal mode detection probability. The results are expected to further optimize the design of OAM-based underwater wireless communication systems.