The rheology of the Earth’s crust controls the long‐term and short‐term strength and stability of plate boundary faults and depends on the architecture and physical properties of crustal materials. In this paper we examine the seismic structure and anisotropy of the crust around the San Andreas Fault (SAF) near Parkfield, California, using teleseismic receiver functions. These data indicate that the crust is characterized by spatially variable and strongly anisotropic upper and middle crustal layers, with a Moho at ∼35 km depth. The upper layer is ∼5–10 km thick and is characterized by strong (≥30%) anisotropy with a slow axis of hexagonal symmetry, where the plane of fast velocity has a strike parallel to that of the SAF and a dip of ∼40∘. We interpret this layer as pervasive fluid‐filled microcracks within the brittle deformation regime. The ∼10–15 km thick midcrustal layer is also characterized by a weak axis of hexagonal symmetry with ≥20% anisotropy, but the dip direction of the plane of fast velocity is reversed. The midcrustal anisotropic layer is more prominent to the northeast of the San Andreas Fault. We interpret the mid crustal anisotropic layer as fossilized fabric within fluid‐rich foliated mica schists. When combined with various other geophysical observations, our results suggest that fault creep behavior around Parkfield is favored by intrinsically weak and overpressured crustal fabric.