In this paper, we present an alternative approach to perform spike sorting of complex brain signals based on spiking neural networks (SNN). The proposed architecture is suitable for hardware implementation by using resistive random access memory (RRAM) technology for the implementation of synapses whose low latency (<1μs) enables real-time spike sorting. This offers promising advantages to conventional spike sorting techniques for brain-computer interfaces (BCI) and neural prosthesis applications. Moreover, the ultra-low power consumption of the RRAM synapses of the spiking neural network (nW range) may enable the design of autonomous implantable devices for rehabilitation purposes. We demonstrate an original methodology to use Oxide based RRAM (OxRAM) as easy to program and low energy (<75 pJ) synapses. Synaptic weights are modulated through the application of an online learning strategy inspired by biological Spike Timing Dependent Plasticity. Real spiking data have been recorded both intra- and extracellularly from an in-vitro preparation of the Crayfish sensory-motor system and used for validation of the proposed OxRAM based SNN. This artificial SNN is able to identify, learn, recognize and distinguish between different spike shapes in the input signal with a recognition rate about 90% without any supervision.