Superradiant gain is the process in which waves are amplified via their interaction with a rotating body, examples including the evaporation of a spinning black hole and electromagnetic emission from a rotating metal sphere. In this Letter we elucidate how superradiance may be realized experimentally in the field of acoustics, and predict the possibility of nonreciprocally amplifying or absorbing acoustic beams carrying orbital angular momentum by propagating them through an absorbing medium that is rotating. We discuss a possible geometry for realizing acoustic superradiant amplification using existing technology.