Tiny but universal beam shifts occur when a polarized light beam is reflected upon a planar interface. Although the beam shifts of Gaussian beams have been measured by the weak measurement technique, the weak measurement for orbital angular momentum (OAM)-induced spatial shifts of vortex beams is still missing. Here, by elaborately choosing the preselection and postselection states, the tiny OAM-induced Goos–Hänchen and Imbert–Fedorov shifts are amplified at an air–prism interface. The maximum shifts along directions both parallel and perpendicular to the incident plane are theoretically predicted and experimentally verified with optimal preselection and postselection states. These maximum shifts can be used to determine the OAM of vortex beams.