Résumé : The efficiency of the slow neutron-capture process in massive stars is strongly influenced by neutron-capture reactions on light elements. At low metallicity, O16 is an important neutron absorber, but the effectiveness of O16 as a light-element neutron poison is modified by competition between subsequent O17(α,n)Ne20 and O17(α,γ)Ne21 reactions. The strengths of key O17(α,γ)Ne21 resonances within the Gamow window for core helium burning in massive stars are not well constrained by experiment. This work presents more precise measurements of resonances in the energy range Ec.m.=612-1319 keV. We extract resonance strengths of ωγ638=4.85±0.79μeV, ωγ721=13.1-2.4+3.2μeV, ωγ814=7.72±0.55meV, and ωγ1318=136±13meV, for resonances at Ec.m.=638, 721, 814, and 1318 keV, respectively. We also report an upper limit for the 612 keV resonance of ωγ<140 neV (95% c.l.), which effectively rules out any significant contribution from this resonance to the reaction rate. From this work, a new O17(α,γ)Ne21 thermonuclear reaction rate is calculated and compared to the literature. The effect of present uncertainties in the O17(α,γ)Ne21 reaction rate on weak s-process yields are then explored using postprocessing calculations based on a rotating 20M⊙ low-metallicity massive star. The resulting O17(α,γ)Ne21 reaction rate is lower with respect to the preexisting literature and found to enhance weak s-process yields in rotating massive star models.