Recent developments in artificial intelligence technology has facilitated advances in neuromorphic computing. Electrical elements mimicking the role of synapses are crucial building blocks for neuromorphic computers. Although various types of two-terminal memristive devices have emerged in the mainstream of synaptic devices, a hetero-synaptic artificial synapse, i.e., one with modulatable plasticity induced by multiple connections of synapses, is intriguing. Here, a synaptic device with tunable synapse plasticity is presented that is based on a simple four-terminal rutile TiO single-crystal memristor. In this device, the oxygen vacancy distribution in TiO and the associated bulk carrier conduction can be used to control the resistance of the device. There are two diagonally arranged pairs of electrodes with distinct functions: one for the read/write operation, the other for the gating operation. This arrangement enables precise control of the oxygen vacancy distribution. Microscopic analysis of the Ti valence states in the device reveals the origin of resistance switching phenomena to be an electrically driven redistribution of oxygen vacancies with no changes in crystal structure. Tuning protocols for the write and the gate voltage applications enable high precision control of resistance, or synaptic plasticity, paving the way for the manipulation of learning efficiency through neuromorphic devices.