Spider silks are remarkable materials designed by nature to have extraordinary elasticity. Their elasticity, however, remains poorly understood, as typical stress-strain experiments only allow access to the axial Young's modulus. In this work, micro-Brillouin light spectroscopy (micro-BLS), a noncontact, nondestructive technique, is utilized to probe the direction-dependent phonon propagation in the Nephila pilipes spider silk and hence solve its full elasticity. To the best of our knowledge, this is the first demonstration on the determination of the anisotropic Young's moduli, shear moduli, and Poisson's ratios of a single spider fiber. The axial and lateral Young's moduli are found to be 20.9 ± 0.8 and 9.2 ± 0.3 GPa, respectively, and the anisotropy of the Young's moduli further increases upon stretching. In contrast, the shear moduli and Poisson's ratios exhibit very weak anisotropy and are robust to stretching.