Understanding star formation rates (SFR) is a central goal of modern star-formation models, which mainly involve gravity, turbulence and, in some cases, magnetic fields (B-fields). However, a connection between B-fields and SFR has never been observed. Here, a comparison between the surveys of SFR and a study of cloud-field alignment - which revealed a bimodal (parallel or perpendicular) alignment - shows consistently lower SFR per solar mass for clouds almost perpendicular to the B-fields. This is evidence of B-fields being a primary regulator of SFR. The perpendicular alignment possesses a significantly higher magnetic flux than the parallel alignment and thus a stronger support of the gas against self-gravity. This results in overall lower masses of the fragmented components, which are in agreement with the lower SFR.