  Using large-scale fully-kinetic two-dimensional particle-in-cell simulations,
we investigate the effects of shock rippling on electron acceleration at
low-Mach-number shocks propagating in high-$\beta$ plasmas, in application to
merger shocks in galaxy clusters. We find that the electron acceleration rate
increases considerably when the rippling modes appear. The main acceleration
mechanism is stochastic shock-drift acceleration, in which electrons are
confined at the shock by pitch-angle scattering off turbulence and gain energy
from the motional electric field. The presence of multi-scale magnetic
turbulence at the shock transition and the region immediately behind the main
shock overshoot is essential for electron energization. Wide-energy non-thermal
electron distributions are formed both upstream and downstream of the shock.
The maximum energy of the electrons is sufficient for their injection into
diffusive shock acceleration. We show for the first time that the downstream
electron spectrum has a~power-law form with index $p\approx 2.5$, in agreement
with observations.
