Natural hazards generate disasters and huge losses in several aspects, with landslides being one of the natural risks that have caused great impacts worldwide. The aim of this research was to explore a method based on machine learning to evaluate susceptibility to rotational landslides in an area near Cuenca city, Ecuador, which has a high incidence of these phenomena, mainly due to its environmental conditions, and in which, however, such studies are scarce. The implemented method consisted of an artificial neural network multilayer perceptron (ANN MLP), generated with the neuralnet R package, with which, by means of different backpropagation algorithms (RPROP+, RPROP−, SLR, SAG, and Backprop), five landslide susceptibility maps (LSMs) were generated for the study area. A landslide inventory updated to 2019 and 10 conditioning factors, mainly topographical, geological, land cover, and hydrological, were considered. The results obtained, which were validated through the AUC-ROC value and statistical parameters of precision, recall, accuracy, and F-Score, showed a good degree of adjustment and an acceptable predictive capacity. The resulting maps showed that the area has mostly sectors of moderate, high, and very high susceptibility, whose landslide occurrence percentages vary between approximately 63% and 80%. In this research, different variants of the backpropagation algorithm were implemented to verify which one gave the best results. With the implementation of additional methodologies and correct zoning, future analyses could be developed, contributing to adequate territorial planning and better disaster risk management in the area.