The use of multi-connectivity has become a useful tool to manage the traffic in heterogeneous cellular network deployments, since it allows a device to be simultaneously connected to multiple cells. The proper exploitation of this technique requires to adequately configure the traffic sent through each cell depending on the experienced conditions. This motivates this work, which tackles the problem of how to optimally split the traffic among the cells when the multi-connectivity feature is used. To this end, the paper proposes the use of a deep reinforcement learning solution based on a Deep Q-Network (DQN) in order to determine the amount of traffic of a device that needs to be delivered through each cell, making the decision as a function of the current traffic and radio conditions. The obtained results show a near-optimal performance of the DQN-based solution with an average difference of only 3.9% in terms of reward with respect to the optimum strategy. Moreover, the solution clearly outperforms a reference scheme based on Signal to Interference Noise Ratio (SINR) with differences of up to 50% in terms of reward and up to 166% in terms of throughput for certain situations. Overall, the presented results show the promising performance of the DQN-based approach that establishes a basis for further research in the topic of multi-connectivity and for the application of this type of techniques in other problems of the radio access network