By exploiting the inherent waveform superposition property of multiple access channel (MAC), over-the-air computation (AirComp) is capable of achieving fast wireless data aggregation, thereby is a promising approach for achieving computation-oriented intelligent services. Reconfigurable intelligent surface (RIS) can be utilized to further enhance the performance of AirComp. However, the joint design of AirComp transceivers and RIS phase shifts is a challenging nonconvex problem due to their coupling with each other. Existing algorithms have a non-scalable computational cost and may suffer performance loss for large-sized problems. In this paper, we propose to use the successive convex approximation (SCA) technique to solve above challenging in a cost-efficient manner. Specificaly, in each iteration, we first adopt the second order Taylor expansion to construct a approximate convex surrogate function of the objective function but with nonconvex constraints, and then use the Lagrange dual method to find a sub-optimal solution for this nonconvex problem. In this manner, we can iteratively update the Lagrange multiplier vector via solving a simple convex problem and the optimization variables with a closed form. Simulation results show that the SCA-based algorithm not only outperforms the conventional approaches in terms of aggregation distortion, but also has much lower computational cost. Also the deployment of RIS can significantly enhance the performance of AirComp.