We study theoretically a dynamics of the ϕ0-Josephson junction, with direct coupling between magnetic moment and Josephson current, which shows features reminiscent of a Kapitza pendulum. We find that, starting with the magnetization along the z-axis, the character of the magnetization dynamics changes crucially as a stable position of the magnetic moment m is realized between the z-and y-axes, depending on the values of the system parameters. Changes in critical current and spin-orbit interaction lead to different stability regions for the magnetization. Excellent agreement is obtained between analytical and numerical results at low values of the Josephson-to-magnetic-energy ratio.

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