We present a deep learning model trained to emulate the radiative transfer during the epoch of cosmological reionization. CRADLE (Cosmological Reionization And Deep LEarning) is an auto-encoder convolutional neural network that uses 2D maps of the star number density and the gas density field at z = 6 as inputs and that predicts 3D maps of the times of reionization t_reion as outputs. These predicted single fields are sufficient to describe the global reionization history of the intergalactic medium in a given simulation. We trained the model on a given simulation and tested the predictions on another simulation with the same parameters but with different initial conditions. The model is successful at predicting t_reion maps that are in good agreement with the test simulation. We used the power spectrum of the t_reion field as an indicator to validate our model. We show that the network predicts large scales almost perfectly but is somewhat less accurate at smaller scales. While the current model is already well suited to get average estimates about the reionization history, we expect it can be further improved with larger samples for the training, better data pre-processing and finer tuning of hyper-parameters. Emulators of this kind could be systematically used to rapidly obtain the evolving H ii regions associated with hydro-only simulations and could be seen as precursors of fully emulated physics solvers for future generations of simulations.