We have measured the form factor ratios r_V = V(0)/A_1(0) and r_2 = A_2(0)/A_1(0) for the decay D_s^+ -> phi ell^+ nu_ell, phi -> K^+ K^-, using data from charm hadroproduction experiment E791 at Fermilab. Results are based on 144 signal and 22 background events in the electron channel and 127 signal and 34 background events in the muon channel. We combine the measurements from both lepton channels to obtain r_V = 2.27 +- 0.35 +- 0.22 and r_2 = 1.57 +- 0.25 +- 0.19.