We report on realization and quantum transport study of a twisted bilayer graphene (tBLG) Josephson junction device. High-quality tBLG employed in the device fabrication is obtained via chemical vapour deposition and the device is fabricated by contacting a piece of tBLG by two closely spaced Al electrodes in an Al-tBLG-Al Josephson junction configuration. Low-temperature transport measurements show that below the critical temperature of the Al electrodes ($T_capprox1.1$ K), the device exhibits sizable supercurrents at zero magnetic field, arising from the superconducting proximity effect with high contact transparency in the device. In the measurements of the critical supercurrent as a function of perpendicularly applied magnetic field, a standard Fraunhofer-like pattern of oscillations is observed, indicating a uniform supercurrent distribution inside the junction. Multiple Andreev reflection characteristics are also observed in the spectroscopy measurements of the device, and their magnetic field and temperature dependencies are found to be well described by the Bardeen$-$Cooper$-$Schrieffer theory.