Topological insulator with antiferromagnetic order can serve as an ideal platform for the realization of axion electrodynamics. In this paper, we report a systematic study of the axion topological insulator candidate EuIn$_2$As$_2$. A linear energy dispersion across the Fermi level confirms the existence of the proposed hole-type Fermi pocket. Spin-flop transitions occur with magnetic fields applied within the $ab$-plane while are absent for fields parallel to the $c$-axis. Anisotropic magnetic phase diagrams are observed and the orientation of the ground magnetic moment is found to be within the $ab$-plane. The magnetoresistivity for EuIn$_2$As$_2$ behaves non-monotonic as a function of field strength. It exhibits angular dependent evolving due to field-driven and temperature-driven magnetic states. These results indicate that the magnetic states of EuIn$_2$As$_2$ strongly affect the transport properties as well as the topological nature.
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