A new mechanism is suggested that draws non-resonant thermal electrons into a higher-velocity range, where they can be effectively accelerated by waves. We argue that the acceleration of a small number of pre-existing resonant particles influences the dynamics of the bulk plasma and results in a macroscopic electric field. The solution for the spatial dependence of this electric field is obtained, and it appears to be a new type of electrostatic shock, which forms only in the presence of background turbulence. This field enriches the region of resonant particles with thermal electrons, which leads to a build-up of an excess of accelerated particles. The number of accelerated particles is calculated. This mechanism appears as a good candidate to explain electron acceleration in the foot of quasi-perpendicular shocks.