We demonstrate a nanowire (NW) phototransistor with synaptic behavior based on inherent persistent photoconductivity. The device is comprised of a single crystalline InAs NW, covered by a native indium oxide layer acting as the photogating layer (PGL). In the negative photoresponse range, the device mimics synaptic neuromorphic behaviors of short-term plasticity, long-term plasticity (LTP), and paired-pulse facilitation. Moreover, the transition from short-term to LTP is observed as the stimulus intensity increases, behaving in accord with the feature of cooperativity. The synaptic behaviors of the device are attributed to the photo-generated electrons trapped/detrapped in the PGL. This NW-based photonic synaptic device would find promising applications in neuromorphic systems and networks.