  A particle acceleration mechanism by radiation pressure of precursor waves in
a relativistic shock is studied. For a relativistic, perpendicular shock with
the upstream bulk Lorentz factor of $\gamma_1 \gg 1$, large amplitude
electromagnetic (light) waves are known to be excited in the shock front due to
the synchrotron maser instability, and those waves can propagate towards
upstream as precursor waves. We find that non-thermal, high energy electrons
and ions can be quickly produced by an action of electrostatic wakefields
generated by the ponderomotive force of the precursor waves. The particles can
be quickly accelerated up to $\epsilon_{\rm max}/\gamma_1 m_e c^2 \sim
\gamma_1$ in the upstream coherent wakefield region, and they can be further
accelerated during the nonlinear stage of the wakefield evolution. The maximum
attainable energy is estimated by $\epsilon_{\rm max}/\gamma_1 m_e c^2 \sim
L_{\rm sys}/(c/\omega_{pe})$, where $L_{\rm sys}$ and $c/\omega_{pe}$ are the
size of an astrophysical object and the electron inertial length, respectively.
