A double-scattering experiment of antiprotons on carbon has been carried out at the Low-Energy Antiproton Ring (LEAR) at CERN, to measure the polarization parameter A p C in antiproton-carbon elastic scattering at small angles. The polarization parameter has been inferred from the azimuthal distribution of the antiprotons after the second scattering. Data have also been collected with a liquid-hydrogen target as the second scatterer, thus allowing the sign of A p C to be determined. The experiment has been performed at two momenta of the extracted antiproton beam, 800 and 1100 MeV/c. A small positive value of the polarization has been observed, compatible with energy independence and a linear increase with the momentum transfer q . Parametrizing A p C as a c q , we get a c = +0.72 0.10 +0.09 ( GeV / c ) −1 . This result is compared with potential model predictions for N̄N amplitudes through a Glauber theory calculation.