[en] The analyzing power, A/sub N/, has been measured for π^+-p→π^+-p at 471, 547, 625, and 687 MeV/c in an angular range corresponding to -0.9 less than or equal to cos theta/sub cm/ less than or equal to 0.8. A polarized proton target with polarization axis normal to the scattering plane was used. The scattered pion and recoil proton were detected in coincidence, using a magnetic spectrometer and a wire chamber/scintillator array, except in cases where one of the particles was kinematically inaccessible. Statistical uncertainties in the data are as low as 0.02; systematic uncertainties are estimated to be less than 3%. The π^-p data are characterized by large values of analyzing power, and rapid variations in the angular distribution with incident momentum. The measurements are compared with the results of existing partial wave analysis