We investigate the topological properties of twisted bilayer superconductors with different even-parity pairings in each layer. In the presence of spin-orbit coupling, the Hamiltonian is mapped into an effective odd-parity superconductor. Based on this, we deduce the topological properties by examining the relative configuration between Fermi surface and Dirac pairing node. We show that mixed Rashba and Dresselhaus spin-orbit coupling and anisotropic hopping terms, which break the C-4 symmetry of the Fermi surface, can induce first-order topological superconductors with non-zero bulk Chern number. This provides a versatile way to control the topological phases of bilayer superconductors by adjusting the twisted angle and chemical potential. We demonstrate our results using a typical twisted angle of 53.13 degrees, at which the translation symmetry is restored and the Chern number and edge state are calculated using the Moire momentum.