With the development of port automation and artificial intelligence, coordination with multi-geographic data centers (Geo-DCs) has become a viable solution to address the issue of limited port computing resources. This study proposes a distributed energy dispatch method for the port microgrid coordinated with Geo-DCs (Geo-DCPM), aimed at reducing port carbon emissions and operational costs. Consider the single point of failure problem and high construction costs of centralized data centers. Geo-DCs are first introduced to solve the problem of insufficient computing resources in ports. An energy consumption calculation model for Geo-DCs is established, considering the data load delay constraint and the data space transfer constraint caused by specific delay-sensitive loads in the port microgrid. Then, an energy dispatch model (EDM) is constructed for the Geo-DCPM, taking into account carbon capture costs. Moreover, based on mixed-integer linear programming, a distributed algorithm is proposed to solve the EDM problem. Finally, the simulation results verify the effectiveness of the proposed method. Compared with the centralized algorithm, the packet loss rate of the distributed algorithm combined with Geo-DCs is significantly lower, reduced by about 70%.