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The synthesis of thin films of magnetic topological materials is necessary to achieve novel quantized Hall effects and electrodynamic responses. EuIn2As2 is a recently predicted topological axion insulator that has an antiferromagnetic ground state and an inverted band structure but that has only been synthesized and studied as a single crystal. We report on the synthesis of c-axis oriented EuIn2As2 films by molecular beam epitaxy on sapphire substrates. By careful tuning of the substrate temperature during growth, we stabilize the Zintl phase of EuIn2As2 expected to be topologically non-trivial. The magnetic properties of these films reproduce those seen in single crystals but their resistivity is enhanced when grown at lower temperatures. We additionally find that the magnetoresistance of EuIn2As2 is negative even up to fields as high as 31T but while it is highly anisotropic at low fields, it becomes nearly isotropic at high magnetic fields above 5T. Overall, the transport characteristics of EuIn2As2 appear similar to those of chalcogenide topological insulators, motivating the development of devices to gate tune the Fermi energy to reveal topological features in quantum transport.