The energy spectra of deuterons recoiling from a deuterium gas target bombarded by transversely polarized 796-MeV protons have been measured to obtain the differential cross sections, dsigma/dt, and analyzing powers, A/sub y/(t), for p-d elastic scattering over a range of laboratory angles from 4.53/sup 0/ to 13.02/sup 0/, corresponding to a range of four-momentum transfer squared, Vertical BartVertical Bar, from 0.013 to 0.108 GeV/sup 2//c/sup 2/. Employing several sets of nucleon-nucleon, N-N, amplitudes obtained from N-N phase shift analyses, comparisons are made between the experimental data and the predictions of a multiple scattering theory. In this region of four-momentum transfer, A/sub y/ is shown to depend almost entirely on the spin-independent and spin-orbit N-N amplitudes.