<p>This study considers the geometric numerical integration of the Ostrovsky equation on a periodic domain. The Ostrovsky equation is a generalization of the well-known Korteweg–de Vries equation and models the propagation of gravity waves in a rotating fluid. Since the Ostrovsky equation involves a mixed derivative, it has an implicit constraint that makes numerical treatment difficult. In this paper, the scalar auxiliary variable (SAV) approach, a recent geometric numerical integration technique, is applied to the Ostrovsky equation to obtain computationally efficient conservative schemes. The SAV approach has been intensively investigated; however, this study is the first attempt to apply it to evolutionary differential equations with a mixed derivative. The resulting schemes preserve the modified invariant corresponding to the energy function of the Ostrovsky equation, satisfy the implicit constraint, and can achieve any order of accuracy. The accuracy and computational efficiency of the resulting schemes are confirmed through numerical experiments. The proposed schemes’ computational cost is very low, almost equivalent to that of explicit exponential integrators.</p>