Distributed Acoustic Sensing (DAS) is a promising technique to improve the rapid detection and characterization of earthquakes. Due to some instrumental limitations, current DAS studies primarily 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 DAS amplitude in different regions follows a similar scaling relation. The scaling relation can provide a rapid magnitude estimation and effectively avoid uncertainties caused by the conversion to ground motions. We finally show that the scaling relation is transferable from one to another new region. The scaling relation highlights the great potential of DAS in earthquake source characterization and early warning.