Undoped cuprates are an abundant class of magnetic insulators, in which the synergy of rich chemistry and sizable quantum fluctuations leads to a variety of magnetic behaviors. Understanding the magnetism of these materials is impossible without the knowledge of the underlying spin model. The typically dominant antiferromagnetic superexchanges can be accurately estimated from the respective electronic transfer integrals. Density functional theory calculations mapped onto an effective one-orbital model in the Wannier basis are an accurate, albeit computationally cumbersome method to estimate such transfer integrals in cuprates. We demonstrate that instead an Artificial Neural Network (ANN), trained on the results of high-throughput calculations, can predict the transfer integrals using the crystal structure as the only input. Descriptors of the ANN model encode the spatial configuration and the chemical composition of the local crystalline environment. A virtual toolbox employing our model can be readily employed to determine leading superexchange paths as well as for rapidly assessing the relevant spin model in yet unknown cuprates.