Antiferromagnetic (AF) metals are rare, yet they combine properties attractive for spintronic devices like robustness against stray fields and electrical readout. Among AF metal oxide candidates, SrCrO₃ remains largely unexplored due to its notoriously difficult synthesis. In this paper, we demonstrate the growth of high-quality SrCrO₃ thin films by magnetron sputtering on substrates that impose a wide range of tensile and compressive strains. Muon spin relaxation experiments, supported by x-ray magnetic dichroism, unveil the emergence of an AF phase with dilute magnetic disorder at low temperatures, while resistivity measurements confirm the simultaneous metallic ground state of SrCrO₃ under low strain. As both compressive and tensile strain increase, a metal-to-insulator transition is induced in the films, while the onset of the magnetic transition temperature remains unchanged. Moreover, an intriguing resistivity upturn, accompanied by a change in the dominant charge-carrier type, occurs at a temperature that correlates with strain. These observations suggest a complex strain-dependent band structure, with strain-induced Jahn-Teller distortions or tilting of the CrO₆ octahedra that emerge depending on the sign of the strain, as inferred from density functional theory calculations.