When the size of State and Action Spaces increases Reinforcement Learning (RL) algorithms may present limitations like the increase in the number of learning episodes that the RL-based agent needs to convergence. Such an increase in the learning process is due to the RL-based agent having to experience more state-action pairs iteratively to achieve a reliable estimation of the value for each state-action pair. Furthermore, RL algorithms could require huge storage space to maintain the experience information. In this vein, Deep Reinforcement Learning (DRL) that leverages both Deep Learning (DL) and RL techniques, arises to overcome RL limitations. DL enables RL to scale to previously intractable decision-making problems (i.e., settings with high-dimensional state and action spaces). Hence, DRL embraces the advantage of function approximators employed in DL to train the learning process and thereby to improve the learning speed and the performance of RL algorithms. Neural Networks (NN) are commonly used as function approximators for generalization of the knowledge acquired by visiting states to other states. The generalization of knowledge allows the agent to learn from a reduced number of interactions with the environment, and therefore the algorithm converges faster. Here, we present DRSIR, a DRL-based solution for routing in SDN that aims to provide intelligent routing while taking advantage of network-state information at the path-level metrics to explore, exploit and learn the best paths when making routing decisions. DRSIR leverages the global view and control of the network furnished by SDN and the interaction with the environment and intelligence provided \ac{DRL}. It computes and installs, in advance, optimal routes in the routing tables of the switches on the Data Plane. Results show that the stretch, link throughput, delay, and packet loss produced by DRSIR outperforms those given by Dijkstra's algorithms when delay, loss, and available bandwidth are individually or jointly used to compute optimal paths. DRSIR is also compared against performance produced by our RL version called RSIR, evincing an improvement regarding the performance metrics evaluated.