The molecular electrostatic potential (MEP) generated by quantum chemistry methods and Gaussian functions is evaluated over graphics processing units (GPUs). This implementation is based on full-range Rys polynomials with nodes and weights obtained in each thread of a GPU. For high angular moments, the corresponding integral is solved using a one-dimension vertical recurrence relation. Thus, we computed the MEP with minimal approximations. We show that this implementation is stable and very efficient since the time consumed over GPUs is quite small compared with similar implementations over CPUs. The implementation was done by using CUDA-C programming techniques within the Graphics Processing Units for Atoms and Molecules (GPUAM) project, which has been designed to analyze quantum chemistry fields over heterogeneous computational resources. With this new scalar field GPUAM is a useful application for the quantum chemistry community, in particular for people interested in chemical reactivity analysis.