An amorphous high-k thin film for a semiconductor device and a manufacturing method thereof are provided. The amorphous high-k thin film includes Bi, Ti, Al, and O. Since a BTAO based amorphous dielectric thin film is used as a dielectric material of a DRAM capacitor, a dielectric constant is more than 25, and an increase of a leakage current caused in reducing a physical thickness of the dielectric thin film can be prevented. Accordingly, it is very useful for the integration of the semiconductor device.