Since Orbital Angular Momentum (OAM) mode can form an infinite N qubit basis, it provides a new coding scheme for communication links. However, ocean turbulence and other external disturbances can cause phase disturbance of OAM mode, which generates the cross talk between the energy states of OAM modes. The self-focusing property of POV is beneficial to the transmission of OAM modes. The transmission quality of POV beams in oceanic turbulence is most related to the beam radius, while it is nearly free from the wavelength, topological charge, and radius-thickness ratio. Because of these special characteristics, POV has attracted wide attention of researchers. Moreover, the absorption of seawater reduces the information carrying capacity of POV photons and weakens the reliability of the system. Therefore, it is necessary to study the absorption of seawater and the transmission characteristics of POV. In addition, the modulation of POV also increases the information capacity carried by the POV's OAM mode. In this paper, the ABEP and information capacity of underwater optical transmission system based on POV carrier and M-PSK modulation are studied under weak absorption turbulence. The wavelength dependence of fading channel is especially considered. The fading channel consists of two parts: signal energy loss caused by seawater turbulence and seawater absorption. Under the condition of paraxial transmission and Rytov approximation, the closed expressions of mean signal-to-noise ratio and signal error probability for M-PSK OAM channel are derived. Considering that the number of OAM signal level channels in common use is far less than the number of OAM topological charge (energy level) of POV vortex carrier, the concept that POV vortex carrier communication link is a symmetric link composed of multiple OAM level channels is proposed. Using the derived expression of ABEP of M-PSK OAM channel and the concept of symmetric link of multi-OAM channel, a novel closed-form expression of ABER and average capacity under various modulation schemes is proposed. Finally, through numerical analysis of the model, new results are draw. The results show that when transmitting over short distances, the wavelength of the photon of the OAM signal of POV has a greater impact on the information capacity of the transmission system than on the absorption of seawater, while when transmitting over long distances, the effect of seawater absorption on the information capacity of the optical transmission system is greater than the wavelength. When the ring radius of the perfect optical vortex increases, the information capacity of the system also increases, and ABEP decreases, but with the increase of the ring radius of POV there is a stable region of ABEP decrease and information capacity increase related to turbulence intensity. The increase in the signal-to-noise ratio of the receiving and transmitting optical systems results in an increase in the information capacity of the system and a decrease in ABEP. The increase of the inner-scale and the decrease of the outer-scale also lead to the increase the information capacity of the system and the decrease of ABEP. In addition, the OAM signal photons of the POV under QPSK modulation are less affected in absorbing weak turbulence links than other orders of modulation. Therefore, on the basis of selecting the appropriate modulation scheme, the ring radius of the POV and the signal-to-noise ratio of the transceiver optical system, which can effectively enhance the information capacity of the OAM signal photon of the POV.