In this paper, we propose a novel design of dielectric laser-driven accelerator (DLA) utilizing evanescent electric field of racetrack ring resonator structures. Driven by laser light with the correctly designed optical phase window, sustained acceleration of electrons with controlled deflection is shown. Based on this design, we calculate an acceleration from 30 keV to 148.312 keV in 104.655 {mu}m using a cascaded 11-stage racetrack ring resonators. This new idea poses a solution for on-chip integration of many DLA stages, while maintains high average accelerating gradients, providing a potential practical realization for accelerator on a chip.