This paper proposes a spatial-temporal recurrent neural network architecture for deep $Q$-networks that can be used to steer an autonomous ship. The network design makes it possible to handle an arbitrary number of surrounding target ships while offering robustness to partial observability. Furthermore, a state-of-the-art collision risk metric is proposed to enable an easier assessment of different situations by the agent. The COLREG rules of maritime traffic are explicitly considered in the design of the reward function. The final policy is validated on a custom set of newly created single-ship encounters called `Around the Clock' problems and the commonly used Imazu (1987) problems, which include 18 multi-ship scenarios. Performance comparisons with artificial potential field and velocity obstacle methods demonstrate the potential of the proposed approach for maritime path planning. Furthermore, the new architecture exhibits robustness when it is deployed in multi-agent scenarios and it is compatible with other deep reinforcement learning algorithms, including actor-critic frameworks.