Anomalous acoustic streaming is observed emanating from sharp edges of solid bodies that are vibrating in fluids. The streaming velocities can be orders of magnitude higher than expected from the Rayleigh streaming at similar amplitudes of vibration. Acoustic velocity of fluid relative to a solid body diverges at a sharp edge, giving rise to a localized time-independent body force acting on the fluid. This force results in a formation of a localized jet. Two-dimensional numerical simulations are performed to predict acoustic streaming for low amplitude vibration using two methods: (1) Steady-state solution utilizing perturbation theory and (2) direct transient solution of the Navier-Stokes equations. Both analyses agree with each other and correctly predict the streaming of a sharp-edged vibrating blade measured experimentally. The origin of the streaming can be attributed to the centrifugal force of the acoustic fluid flow around a sharp edge. The dependence of this acoustic streaming on frequency and velocity is examined using dimensional analysis. The dependence law is devised and confirmed by numerical simulations.