Shock drift acceleration (SDA) plays an important role in generating high-energy electrons at quasi-perpendicular shocks, but its efficiency in low-beta plasmas is questionable. In this article, we perform a two-dimensional particle-in-cell simulation of a low-Mach-number, low-plasma-beta quasi-perpendicular shock, and find that the electron cyclotron drift instability is unstable at the leading edge of the shock foot, which is excited by the relative drift between the shock-reflected ions and the incident electrons. The electrostatic waves triggered by the electron cyclotron drift instability can scatter and heat the incident electrons, which facilitates their escape from the shock’s loss cone. These electrons are then reflected by the shock and energized by SDA. In this way, the acceleration efficiency of SDA at low-plasma-beta quasi-perpendicular shocks is highly enhanced.