A magnetic surface acoustic wave (SAW) sensor is built by growing a 100 nm galfenol (Fe72Ga28) film by sputtering between the interdigitated transducers of a SAW delay line. Love waves are produced when the shear waves excited on the piezoelectric substrate are guided by a 3.1 μm layer of amorphous SiO2. Due to the magnetostrictive nature of galfenol deposited on top, the application of magnetic fields modulates the propagation of the mechanical excitations along the sensor by the strain coupling. By introducing the delay line in a feedback loop circuit, these changes are studied as resonant frequency variations. Magnetic field cycles of ±40 mT are applied to the sample and the resonant frequency shift is tracked simultaneously. The sensor exhibited hysteretic frequency behavior that depends on the orientation of the applied magnetic field relative to the direction of Love wave propagation. In the configuration in which the wave vector and the applied field form an angle of 45°, the resonant frequency seems to increase with the magnetization induced by the external field. When the wave vector propagation is parallel to the field, two positive peaks appear close to the coercive field of the film, which has not been reported before. This is probably due to a more complex relationship between the acoustic wave and the magnetic state of the film which could be exploited to give rise to new models of magnetic sensors.