The paper presents a random vibration analysis of a U-Oscillating Water Column wave energy harvester (U-OWC). The U-OWC comprises a vertical duct on the wave beaten side, in addition to the elements of conventional OWCs. From a mathematical perspective, the U-OWC dynamic response is governed by a set of coupled non-linear differential equations with asymmetric matrices of mass, damping, and stiffness. In this work, an approximate analytical solution of the U-OWC equations of motion is sought by using the technique of statistical linearization. This technique allows pursuing rapid random vibration analyses via classical linear input-output relationships. The analysis is conducted by considering the case of the full-scale prototype in the port of Civitavecchia (Rome, Italy). The reliability of the proposed approach is assessed versus relevant Monte Carlo data. For this, realizations of sea states compatible with typical power spectral density functions of sea waves are employed. The performed analyses prove that the statistical linearization technique based approach is an efficient and reliable tool which may both circumvent the use of time-consuming Monte Carlo simulations, and be used for a variety of design optimization related parameter studies.