  Radio relics associated with merging galaxy clusters indicate the
acceleration of relativistic electrons in merger-driven shocks with low sonic
Mach numbers ($M_{\rm s}\lesssim 3$) in the intracluster medium (ICM). Recent
studies have suggested that electron injection to diffusive shock acceleration
(DSA) could take place through the so-called Fermi-like acceleration in the
shock foot of $\beta=P_{\rm gas}/P_{\rm B}\approx 20-100$ shocks and the
stochastic shock drift acceleration (SSDA) in the shock transition of
$\beta\approx 1-5$ shocks. Here we explore how the SSDA can facilitate electron
preacceleration in weak quasi-perpendicular ($Q_{\perp}$) shocks in
$\beta\approx 20-100$ plasmas by performing particle-in-cell simulations in the
two-dimensional domain large enough to encompass ion-scale waves. We find that
in supercritical shocks with $M_{\rm s}\gtrsim M_{\rm AIC}^*\sim 2.3$,
multi-scale waves are excited by the ion and electron temperature anisotropies
in the downstream of the shock ramp, and that through stochastic pitch-angle
scattering off the induced waves, electrons are confined in the shock
transition for an extended period. Gaining energy through the gradient-drift
along the motional electric field, electrons could be preaccelerated all the
way to injection to DSA at such ICM shocks. Our findings imply that the
electron DSA process at weak ICM shocks could explain the origin of radio
relics. However, a further investigation of electron acceleration at
subcritical shocks with $M_{\rm s}< 2.3$ is called for, since the Mach numbers
of some observed radio relic shocks derived from radio or X-ray observations
are as low as $M_{\rm s}\sim 1.5$.
