Stochastic computing has shown promising results for low-power area-efficient hardware implementations of neural networks. In particular, probabilistic methods are being actively explored in models of spiking neural processing systems for enabling noisy and low-precision hardware neuromorphic computing architectures to implement state-of-the-art recognition and inference systems. It is therefore important to develop suitable sources of stochastic behavior for these neural processing systems that will allow them to maintain their compact and low-power benefits. Here we present a mixed-mode analog-digital circuit that can be used to control the amount of variability produced by event-based spiking neural networks, which exploits the inherent device-mismatch properties of the analog circuits used in combination with the spiking nature of the neural network. We characterize the properties of the circuit presented and demonstrate its applicability in a neuromorphic processor device comprising 256 adaptive integrate and fire neurons and 256 × 256 dynamic synapses.