This paper presents a state-feedback-based backstepping control algorithm to address the point stabilization (or setpoint regulation) control problem for an underactuated autonomous underwater vehicle (AUV) in the presence of constant and irrotational ocean current disturbance. A nonlinear three degree of freedom dynamic model in the horizontal plane for an AUV without symmetry fore/aft is considered. The expression of the relationship between the desired heading angle of the AUV and direction angle of the ocean current, which is a necessary condition for precise point stabilization control of an underactuated AUV in the presence of ocean current disturbance is firstly discussed in this paper. The proposed backstepping control law for point stabilization has further been enriched by incorporating an additional integral action for enhancing the steady state performance of the AUV control system, while practical asymptotic stability analysis of the system is carried out using Lyapunov theory and Barbalat's Lemma. Simulation experiments of an underactuated AUV verify the theorem proposed and demonstrate the effectiveness of the controller.