This paper investigates the usage of unmanned aerial vehicles (UAV s) as relays for data transmission in vehicular networks. We are motivated to address the challenges induced by the lack of direct communication between the vehicles and the infrastructures, such as signal coverage limitations and the existence of obstacles. We consider a scenario in which UAV relays perform cooperative communication in vehicular networks to offer extended coverage to the vehicles, which results in an improvement in the system capacity and reliability. Identifying an efficient UAV-assisted collaboration strategy for vehicular networks is challenging due to the vehicle mobility and the limited power consumption of UAVs. To tackle this problem, we propose a UAV-assisted cooperative relaying scheme based on deep reinforcement learning. To this end, we first determine the optimal transmit powers of a given set of UAV relays to maximize the total throughput of the system. Then, we formulate the UAV-assisted cooperative relaying process as a Markov process and apply a deep Q-network to obtain an effective UAV relay selection strategy. One of the advantages of our solution is that it does not require the knowledge of the vehicle moving trajectories. Through simulations, we demonstrate the effectiveness of our proposed method.