With Rytov approximation theory, we derive the analytic expression of detection probability of Airy vortex beam carrying orbital angular momentum (OAM) through an anisotropic weak oceanic turbulence. We investigate the influences of turbulence parameters and beam parameters on the propagation properties of Airy-OAM beam. The numerical simulation results show that the anisotropic oceanic turbulence with a lower dissipation rate of temperature variance, smaller ratio of temperature and salinity contributions to the refractive index spectrum, higher dissipation rate of kinetic energy per unit mass of fluid, bigger inner scale factor, larger anisotropic coefficient causes the larger detection probability of Airy-OAM beam. Moreover, the Airy-OAM beam with a smaller topological charge, larger main ring radius and longer wavelength, has strong resistance to oceanic turbulent interference. Additionally, the detection probability decreases with the increase of receiving aperture size. In comparison with Laguerre-Gaussian-OAM beam, Airy-OAM beam has more anti-interference to turbulence when its topological charge is larger than 5 due to its non-diffraction and self-healing characteristics. The results are useful for underwater optical communication link using Airy-OAM beam.