In recent years, with the development of underwater laser communication, laser imaging, lidar and other technologies, many scholars have carried out extensive research on the propagation of beams in ocean turbulence. Beams propagation in ocean medium is greatly affected by ocean turbulence, and the orbital angular momentum multiplexing of the vortex beam greatly increases the system capacity, thus it is of great significance to investigate the propagation of the vortex beam in ocean turbulence. Most of the previous studies have focused on the propagation of beams through horizontal ocean turbulence. However, the beam is mostly propagated through ocean turbulence in the slant path in practical applications. Based on the theory of horizontal ocean turbulence, the phase screen of ocean turbulence in the slant path is generated and compensated, the correctness of ocean turbulence phase screen in the slant path is demonstrated by phase structure function. The uplink propagation link model of collimated Gaussian vortex beam in ocean turbulence is built based on the multi-phase screen method. The intensity and phase profiles, beam wander, on-axis scintillation index and long-exposure beam radius of the collimated Gaussian vortex beam in the slant path of ocean turbulence for the values of the different zenith angle, the inner scale and the outer scale of oceanic turbulence, topological charge and other ocean turbulence parameters are numerically simulated and analyzed. Two-dimensional diagram of random ocean turbulence phase screen (Fig.2(a)), and the correctness of ocean turbulence phase screen in slant path is demonstrated by phase structure function (Fig.2(b)); The beam wander of collimated Gaussian vortex beam versus the propagation distance for the values of different tidal velocity of depth-averaged is simulated (Fig.6(b)); The beam wander of the collimated Gaussian vortex beam versus the propagation distance for the values of different wind speed, the zenith angle and the outer scale of oceanic turbulence is simulated (Fig.7). The on-axis scintillation index of the collimated Gaussian vortex beam versus the propagation distance for the values of different inner scale and the outer scale of oceanic turbulence is simulated (Fig.8(b)). The correctness of ocean turbulence phase screen in slant path is demonstrated by phase structure function. The uplink propagation link model of ocean turbulence is simulated by multi-phase screen method. The results show that the smaller the topological charges and the larger the inner scale and the outer scale of oceanic turbulence the vortex beam, the greater the influence of turbulence on the beam is; The beam wander, the on-axis scintillation index and the long-exposure beam radius of collimated Gaussian vortex beam increase with the increase of the outer scale of ocean turbulence. Ideally, the outer scale of ocean turbulence is taken as infinity to overestimate the effect of ocean turbulence on the beam. The beam wander and the on-axis scintillation index are mainly affected by the propagation distance in the uplink propagation of ocean turbulence; Moreover, because of the characteristics of the vortex beam, the topological charges and the long-exposure beam radius have significant effects on the intensity and phase profiles and the long-exposure beam radius.