The acceleration of the co-current toroidal rotations around resonant surfaces by resonant magnetic perturbations (RMPs) through turbulence is presented. These experiments were performed using a Langmuir probe array in the edge plasmas of the J-TEXT tokamak. This study aims at understanding the RMP effects on edge toroidal rotations and exploring its control method. With RMPs, the flat electron temperature Te profile due to magnetic islands appears around resonant surfaces [K. J. Zhao et al., Nucl Fusion, 55, 073022 (2015)]. When the resonant surface is closer to the last closed flux surface, the flat Te profile vanishes with RMPs. In both cases, the toroidal rotations significantly increase in the direction of the plasma current around resonant surfaces with RMPs. The characteristics of turbulence are significantly affected by RMPs around resonant surfaces. Turbulence intensity profile changes and the poloidal wave vector kθ increases with RMPs. The power fraction of the turbulence components in the ion diamagnetic drift direction increases with RMPs. 2The measurements of turbulent Reynolds stresses are consistent with that the toroidal flows can be driven by turbulence. The estimations of the energy transfer between turbulence and toroidal flows suggest that turbulence energy transfers into toroidal flows. The result has the implication of the intrinsic rotation being driven by RMPs via turbulence.