The Doppler-shifted cyclotron resonance (ω−kzvz=Ωf) between fast ions and shear Alfvén waves is experimentally investigated (ω, wave frequency; kz, axial wavenumber; vz, fast-ion axial speed; Ωf, fast-ion cyclotron frequency). A test particle beam of fast ions is launched by a Li+ source in the helium plasma of the LArge Plasma Device (LAPD) [W. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs, Rev. Sci. Instrum. 62, 2875 (1991)], with shear Alfvén waves (SAW) (amplitude δ B/B up to 1%) launched by a loop antenna. A collimated fast-ion energy analyzer measures the nonclassical spreading of the beam, which is proportional to the resonance with the wave. A resonance spectrum is observed by launching SAWs at 0.3–0.8ωci. Both the magnitude and frequency dependence of the beam-spreading are in agreement with the theoretical prediction using a Monte Carlo Lorentz code that launches fast ions with an initial spread in real/velocity space and random phases relative to the wave. Measured wave magnetic field data are used in the simulation.