Twisted van der Waals (vdW) heterostructures offer a unique platform for engineering the efficient Josephson coupling between cuprate thin crystals harboring the nodal superconducting order parameter. Preparing the vdW heterostructures-based Josephson junction comprising stacked cuprates requires maintaining an ordered interface with preserved surface superconductivity. Here, we report the preparation of the Josephson junction out of the stacked Bi₂Sr₂CaCu₂O_8+d crystals using the cryogenic dry transfer technique and encapsulating the junction with an insulating layer, that protects the interface during the electrical contacts evaporation at the 1 × 10⁻⁶ mbar base pressure. We find that the Josephson critical current I_c has a maximum at low twist angles, comparable to that of the bulk intrinsic Josephson junctions, and is reduced by two orders of magnitude at twist angles close to 45°. The reduction of I_c occurs due to a mismatch between superconducting d-wave order parameters, which suppresses the direct Cooper pair tunneling.