With the explosive demands for data, content delivery networks are facing ever-increasing challenges to meet end-users' quality-of-experience requirements, especially in terms of delay. Content can be migrated from surrogate servers to local caches closer to end-users to address delay challenges. Unfortunately, these local caches have limited capacities, and when they are fully occupied, it may sometimes be necessary to remove their lower-priority content to accommodate higher-priority content. At other times, it may be necessary to return previously removed content to local caches. Downloading this content from surrogate servers is costly from the perspective of network usage, and potentially detrimental to the end-user QoE in terms of delay. In this paper, we consider an edge content delivery network with vehicular nodes and propose a content migration strategy in which local caches offload their contents to neighboring edge caches whenever feasible, instead of removing their contents when they are fully occupied. This process ensures that more contents remain in the vicinity of end-users. However, selecting which contents to migrate and to which neighboring cache to migrate is a complicated problem. This paper proposes a deep reinforcement learning approach to minimize the cost. Our simulation scenarios realized up to a 70% reduction of content access delay cost compared to conventional strategies with and without content migration.