The intensity and scintillation index of vortex beams propagating in the oceanic turbulence are simulated by using a step-by-step phase screen method. We find that the vortex beam spot diffuses gradually and the central dark spot gradually disappears with increase in the propagation distance. By changing the parameters of the turbulent phase screen to simulate the oceanic turbulence with different strengths, we find that the on-axis scintillation index of the vortex beam increases with increase of the mean-square temperature dissipation rate, increase of the relative strength of temperature and salinity fluctuations, or decrease of turbulent kinetic energy dissipation rate per unit mass of fluid. The scintillation index of the vortex beam is lower than that of the Gaussian beam when the propagation distance reaches a certain value, and the larger the topological charge is, the more rapidly the scintillation index descends.