Biological neurons can detect complex spatio-temporal features in spiking patterns via their synapses spread across across their dendritic branches. This is achieved by modulating the efficacy of the individual synapses, and by exploiting the temporal delays of their response to input spikes, depending on their position on the dendrite. Inspired by this mechanism, we propose a neuromorphic hardware architecture equipped with multiscale dendrites, each of which has synapses with tunable weight and delay elements. Weights and delays are both implemented using Resistive Random Access Memory (RRAM). We exploit the variability in the high resistance state of RRAM to implement a distribution of delays in the millisecond range for enabling spatio-temporal detection of sensory signals. We demonstrate the validity of the approach followed with a RRAM-aware simulation of a heartbeat anomaly detection task. In particular we show that, by incorporating delays directly into the network, the network's power and memory footprint can be reduced by up to 100x compared to equivalent state-of-the-art spiking recurrent networks with no delays.