Advances in non-volatile resistive switching random access memory (RRAM) have made it a promising memory technology with potential applications in low-power and embedded in-memory computing devices owing to a number of advantages such as low-energy consumption, low area cost and good scaling. There have been proposals to employ RRAM in architecting chips for neuromorphic computing and artificial neural networks where matrix-vector multiplication can be computed in the analog domain in a single timestep. However, it is challenging to employ RRAM devices in neuromorphic chips owing to the non-ideal behavior of RRAM. In this article, we propose a cycle-accurate and scalable system-level simulator that can be used to study the effects of using RRAM devices in neuromorphic computing chips. The simulator models a spatial neuromorphic chip architecture containing many neural cores with RRAM crossbars connected via a Network-on-Chip (NoC). We focus on system-level simulation and demonstrate the effectiveness of our simulator in understanding how non-linear RRAM effects such as stuck-at-faults (SAFs), write variability, and random telegraph noise (RTN) can impact an application’s behavior. By using our simulator, we show that RTN and write variability can have adverse effects on an application. Nevertheless, we show that these effects can be mitigated through proper design choices and the implementation of a write-verify scheme.