Galaxies are thought to be fed by the continuous accretion of intergalactic gas, but direct observational evidence has been elusive. The accreted gas is expected to orbit about the galaxy's halo, delivering not just fuel for star formation but also angular momentum to the galaxy, leading to distinct kinematic signatures. We report observations showing these distinct signatures near a typical distant star-forming galaxy, where the gas is detected using a background quasar passing 26 kiloparsecs from the host. Our observations indicate that gas accretion plays a major role in galaxy growth because the estimated accretion rate is comparable to the star-formation rate.