A new approach is proposed for measuring the local dispersion curves of surface waves in weakly anisotropic media using a single, multi-component station, which consists of translation and rotation or strain. We directly extract the local azimuth-dependent phase velocity of the Rayleigh wave from the 6C amplitude ratio using seismic arrays deployed in Southern California. The extracted dispersion curves match well with the theoretical 2φ azimuthal anisotropy term. And the estimated fast wave direction is also consistent well with results calculated from SKS and beamforming methods which demonstrates the feasibility of studying local seismic anisotropy directly from 6C amplitude observations.