Distributed Acoustic Sensing (DAS) is a promising technique to improve the rapid detection and characterization of earthquakes. Previous DAS studies mainly focus on the phase information but less on the amplitude information. In this study, we compile earthquake data from two DAS arrays in California, USA, and one submarine array in Sanriku, Japan. We develop a data-driven method to obtain the first scaling relation between DAS amplitude and earthquake magnitude. Our results reveal that the earthquake amplitudes recorded by DAS in different regions follow a similar scaling relation. The scaling relation can provide a rapid earthquake magnitude estimation and effectively avoid uncertainties caused by the conversion to ground motions. Our results show that the scaling relation appears transferable to new regions with calibrations. The scaling relation highlights the great potential of DAS in earthquake source characterization and early warning.