  The first measurements of the induced proton polarization, P_n, for the 12C
(e,e'\vec{p}) reaction are reported. The experiment was performed at quasifree
kinematics for energy and momentum transfer (\omega,q) \approx (294 MeV, 756
MeV/c) and sampled a recoil momentum range of 0-250 MeV/c. The induced
polarization arises from final-state interactions and for these kinematics is
dominated by the real part of the spin-orbit optical potential. The
distorted-wave impulse approximation provides good agreement with data for the
1p_{3/2} shell. The data for the continuum suggest that both the 1s_{1/2} shell
and underlying l > 1 configurations contribute.
