Self-induced rotary sloshing caused by an upward off-centered jet in a cylindrical container is numerically and experimentally investigated. Unlike the regular jet-induced rotary sloshing, the present off-centered case could contain components of higher fluctuation in the surface wave and the amplitude exhibits different values in various view angles. A simple geometrical model for the amplitude is established, by assuming the conservation of the angular momentum of the sloshing wave, and the predicted amplitude is tested against the experimental and computational results. Some results for the flow pattern, sloshing period, possible occurrence regime and trajectory of the peak point of the free surface swell due to the inlet jet are given.