Two-dimensional ferroelectric α-In₂Se₃ possesses many fascinating physical properties. However, chemical-vapor-deposited ferroelectric α-In₂Se₃ typically requires high temperatures (>650 ℃). In this work, α-In₂Se₃ is synthesized at 400 to 460 ℃ by introducing a KCl/LiCl/NH₄Cl ternary catalyst, resulting in a 200 ℃ reduction in growth temperature compared with ferroelectric α-In₂Se₃ synthesized by the traditional chemical vapor deposition (CVD) method. The surface morphology of the as-prepared material is controlled by temperature and gas flow rate. As the growth temperature increases from 400 to 460 ℃, the synthesized α-In₂Se₃ is changed from discrete hexagonal flakes to a continuous and uniform thin film, which is confirmed by the scanning electron microscope. Raman spectroscopy shows that the characteristic peaks of In₂Se₃ are located at 103, 180, and 195 cm^–1, respectively, indicating that the CVD-grown In₂Se₃ is α-phase. Furthermore, energy dispersive spectrometer and X-ray photoelectron spectroscopy indicate that the elemental composition is close to the ideal stoichiometric ratio, confirming the successful synthesis of the α-In₂Se₃. Then, the as-prepared α-In₂Se₃ is transferred onto Si/SiO₂ substrate for device fabrication. Atomic force microscope indicates that the film is uniform, with an approximate thickness of 63 nm. The fabricated two-terminal memristors exhibit analogous resistive switching behaviors. And such memristors are used to achieve synaptic functions of long-term potentiation/long-term depression. For artificial neural network simulations based on the synaptic memristors, the recognition accuracy for hand-written digit image exceeds 90%. This work provides a practical method for growing two-dimensional ferroelectric α-In₂Se₃ at low temperatures for applications in synaptic devices and neuromorphic computing.