We present a study of the east-west anisotropy of trapped-proton fluxes in low-Earth orbit based on the measurements of the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) experiment. The differential intensities of eastward- and westward-traveling protons detected in the South Atlantic Anomaly region were estimated as a function of equatorial pitch angle and drift shell, for six energy bins between 80 MeV and 2 GeV. We found that, as a consequence of the strong atmospheric gradient coupled with the large gyroradius in this energy range, the intensities of eastward fluxes exceed those of westward fluxes by a factor of similar to 10-20. However, the reported directional asymmetry also depends on the sign of the local flux gradient, resulting in more intense westward fluxes beyond the radial distances where the inner belt peaks. PAMELA observations can be used to improve the description of the near-Earth radiation environment at lowest altitudes and highest trapping energies, where current theoretical and empirical models are affected by the largest uncertainties.