This paper develops an energy management system (EMS) for an artificial intelligence (AI) data center coexisting with renewable energy. Under a cost-minimization framework, the EMS for a renewable energy coexisting data center (RCDC) jointly optimizes AI task scheduling, on-site renewable energy utilization, and electricity market participation. It maximizes the economic benefits of RCDC operation under both wholesale and retail market participation models. Empirical evaluations using real-world electricity prices, data center power consumption, and renewable energy generation tracking data demonstrate significant electricity cost savings resulting from the coexistence of renewable energy and AI data centers.