Dexterous manipulation in robotic hands relies on an accurate sense of artificial touch. Here we investigate neuromorphic tactile sensation with an event-based optical tactile sensor combined with spiking neural networks for edge orientation detection. The sensor incorporates an event-based vision system (mini-eDVS) into a low-form factor artificial fingertip (the NeuroTac). The processing of tactile information is performed through a Spiking Neural Network with unsupervised Spike-Timing-Dependent Plasticity (STDP) learning, and the resultant output is classified with a 3-nearest neighbours classifier. Edge orientations were classified in 10-degree increments while tapping vertically downward and sliding horizontally across the edge. In both cases, we demonstrate that the sensor is able to reliably detect edge orientation, and could lead to accurate, bio-inspired, tactile processing in robotics and prosthetics applications.