In the framework of continuum mechanics, the linear peridynamic theory is a nonlocal approach to study homogeneous deformations in microelastic materials. The principal physical characteristic of such material model is that it accounts for the effects of long-range forces and as a consequence its solutions profile shows dispersive effects. In particular, the stiffness of the material in the presence of long-range forces is incorporated in the micromodulus function. An important issue in this setting consists in deriving the shape of such a function as it measures the non lacality of the model. Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this context, we propose to apply radial basis functions (RBFs) as activation functions in suitably designed Physics Informed Neural Networks (PINNs) to solve the inverse problem of computing the perydinamic kernel in the nonlocal formulation of classical wave equation. We show that the selection of a RBF is necessary to achieve meaningful solutions and that, with classical choices, non admissible solutions are provided. We support our results with numerical examples and experiments, comparing the solution obtained with the proposed RBF-PINN to the exact solutions.