Semi-magnetic topological insulators have received wide attention because of their unique electrical properties, including the emergent half-quantized linear Hall effect. However, nonlinear Hall effects in these materials have not been studied. In this work, the nonlinear Hall effect in semi-magnetic topological insulators is investigated, and its dependence on the orientation of the magnetic moment in the magnetic layer is explored. By using both analytical method and numerical method, it is demonstrated that the nonlinear Hall conductance is more sensitive to the horizontal component of the magnetic moment than the linear Hall conductance, which predominantly depends on the vertical component of the magnetic moment. Our results reveal that the nonlinear Hall conductance can serve as a sensitive probe to detect changes in the orientation of the magnetic moment in experiments. Specifically, it is shown that the nonlinear Hall effect is governed by the Berry dipole moment, whose magnitude and direction vary with the tilt of the magnetic moment, thereby offering a unique signature of its orientation. The potential for using both linear and nonlinear Hall effects to map the direction of the magnetic moment in semi-magnetic topological insulators is highlighted in this work. Besides, the measurement of the nonlinear Hall effect can be directly implemented using existing experimental setups, without the need for additional modifications. The findings offer insights into the quantum transport behavior of the semi-magnetic topological insulator and pave the way for new experimental techniques to manipulate and probe their magnetic properties.