In this work, the first surface acoustic-wave-based magnetic field sensor using thin-film AlScN as piezoelectric material deposited on a silicon substrate is presented. The fabrication is based on standard semiconductor technology. The acoustically active area consists of an AlScN layer that can be excited with interdigital transducers, a smoothing SiO2 layer, and a magnetostrictive FeCoSiB film. The detection limit of this sensor is 2.4 nT/Hz at 10 Hz and 72 pT/Hz at 10 kHz at an input power of 20 dBm. The dynamic range was found to span from about ±1.7 mT to the corresponding limit of detection, leading to an interval of about 8 orders of magnitude. Fabrication, achieved sensitivity, and noise floor of the sensors are presented.