Many alignment methods, including reinforcement learning from human feedback (RLHF), rely on the Bradley-Terry reward assumption, which is insufficient to capture the full range of general human preferences. To achieve robust alignment with general preferences, we model the alignment problem as a two-player zero-sum game, where the Nash equilibrium policy guarantees a 50% win rate against any competing policy. However, previous algorithms for finding the Nash policy either diverge or converge to a Nash policy in a modified game, even in a simple synthetic setting, thereby failing to maintain the 50% win rate guarantee against all other policies. We propose a meta-algorithm for language model alignment with general preferences, inspired by convergent algorithms in game theory. Theoretically, we prove that our meta-algorithm converges to an exact Nash policy. Additionally, our meta-algorithm is simple and can be integrated with many existing methods designed for RLHF and preference optimization with minimal changes. Experimental results demonstrate the effectiveness of the proposed framework when combined with existing preference policy optimization methods.