A complete set of analyzing powers has been obtained for ${}^{12}\mathrm{C}{(}^{7}\mathrm{Li}\ensuremath{\rightarrow}{,}^{7}\mathrm{Li}{)}^{12}\mathrm{C}$ elastic scattering at a bombarding energy of 34 MeV. Optical model calculations using standard forms for the spin-orbit and tensor potentials are unable to simultaneously describe all the available data. However, coupled-discretized-continuum-channels (CDCC) calculations using cluster-folding model form factors provide a reasonable overall description of the data with only two adjustable parameters. Reorientation effects are extremely important in obtaining a good description of the analyzing powers, with the reorientation coupling of the ${}^{7}\mathrm{Li}$ ground state being a major contributor to all the analyzing powers and the main source of the second-rank tensor analyzing powers ${T}_{20},$ ${T}_{21},$ and ${T}_{22}.$ The failure of optical model calculations to describe the second rank data implies that the effect of this reorientation coupling cannot be described accurately by means of a dynamic polarization potential constrained to be of the standard forms. The CDCC calculations also demonstrate the effect of coupling to the $\ensuremath{\alpha}\ensuremath{-}t$ continuum on the analyzing powers.