In the direct-arrival zone in deep water, the sound ray arrival angle is one of the most important properties of the sound field. However, it is complicated to estimate the arrival angle only by using the information about the sound pressure. Vector sensors have significant advantages in direction-of-arrival estimation, and the acoustic energy flux detection is one of the most important estimation methods. In this paper, the properties of complex acoustic intensity in the direct-arrival zone in deep water are analyzed, and the arrival angles of sound rays are estimated with the complex acoustic intensity extracted from the experimental data. Firstly, the expressions of horizontal particle velocity, vertical particle velocity and complex sound intensity are provided based on the ray theory. It is shown that the amplitudes of the horizontal and vertical particle velocities and the components of the complex sound intensity are closely related to the sound ray arrival angle. The larger the sound ray arrival angle, the greater the vertical particle velocity and the vertical component of the complex sound intensity are, but the weaker the horizontal particle velocity and the horizontal component of the complex sound intensity are. Secondly, for the direct-arrival zone of the sound field generated by a shallow source in deep water, the properties of the complex sound intensity with deep receiver are analyzed based on the sound ray arrival structure. The theoretical and simulation results show that the arrival angles of the sound rays can be estimated with the complex sound intensities of pulses received by a deep receiver. The mean arrival angles of the direct ray and the surface-reflected ray can be estimated with the complex sound intensities of the pulses of the direct-arrival wave and the surface-reflected wave. The mean arrival angles of the bottom-reflected ray and the surface-reflected-bottom-reflected ray can be estimated with the complex sound intensities of the pulses of the bottom-reflected wave and the surface-reflected-bottom-reflected wave. The angle obtained with the complex sound intensity of the total field comprised of all sound rays is approximately equal to the mean arrival angles of the direct ray and the surfaced-reflected ray. Thirdly, the validity of the arrival angle estimation with the complex sound intensity is verified by the experimental data. During a deep water experiment conducted in 2014, a vector sensor was placed at a depth of 3146 m to receive the experimental signals. Within the range of 17 km, the vector sensor received the direct ray from the sound source towed at about 140 m. By using the pulses of the direct-arrival wave and the surface-reflected wave received by the vector sensor, the mean arrival angles of the direct rays and the surface-reflected rays are estimated. It is shown that the estimated arrival angles are consistent with the theoretical results.