In this paper, we consider a reconfigurable intelligent surface (RIS)-assisted two-way relay network, in which two users exchange information through the base station (BS) with the help of an RIS. By jointly designing the phase shifts at the RIS and beamforming matrix at the BS, our objective is to maximize the minimum signal-to-noise ratio (SNR) of the two users, under the transmit power constraint at the BS. We first consider the single-antenna BS case, and propose two algorithms to design the RIS phase shifts and the BS power amplification parameter, namely the SNR-upper-bound-maximization (SUM) method, and genetic-SNR-maximization (GSM) method. When there are multiple antennas at the BS, the optimization problem can be approximately addressed by successively solving two decoupled subproblems, one to optimize the RIS phase shifts, the other to optimize the BS beamforming matrix. The first subproblem can be solved by using SUM or GSM method, while the second subproblem can be solved by using optimized beamforming or maximum-ratio-beamforming method. The proposed algorithms have been verified through numerical results with computational complexity analysis.