The analyzing power for proton-carbon elastic scattering in the Coulomb-nuclear interference region of momentum transfer, 9.0x10(-3)<-t<4.1x10(-2) (GeV/c)(2), was measured with a 21.7 GeV/c polarized proton beam at the Alternating Gradient Synchrotron of Brookhaven National Laboratory. The ratio of hadronic spin-flip to nonflip amplitude, r(5), was obtained from the analyzing power to be Rer(5)=0.088+/-0.058 and Imr(5)=-0.161+/-0.226.