Distributed acoustic sensing (DAS) acquisition measures the ground motion using fiber-optic cables. Unlike conventional sensors, DAS can cost effectively provide dense seismic arrays and long-term operations, which is good for monitoring ambient noise. We propose a similarity-weighted stacking of randomly selected short-time duration noise to generate virtual common-shot-gathers (CSG). The similarity-weighted stacking only counts the primary contributions of coherent events, while a short-time correlation can suppress the crosstalk usually presents in late arrivals. Then, we use the wave-equation Rayleigh-wave dispersion-spectrum inversion, which utilizes all the dispersion modes available and avoids picking the dispersion curve, estimating the shallow S-wave velocities. We use a field DAS data set collected in Saudi Arabia to demonstrate the proposed method.