How we can calculate the spin-orbit coupling? I need to know which package is more suitable for spin-orbit coupling calculation, Gaussian package or GAMESS package or anything else suggestion?
It depends on what kind of system you are dealing with and what you want to calculate, but for example the DFT codes VASP (plane wave basis) and the GREEN-SIESTA implementation of the SIESTA code (atomic orbital basis) can deal quite successfully with SOC. The KKR code by the Budapest-Vienna group, for example, is fully relativistic and solves the Dirac equation directly, so the SOC is properly addressed there. Many other modern DFT codes also include SOC implementations (WIEN2k, Quantum Espresso, ABINIT, etc.), but I'm not so familiar with them.
Spin-orbit coupling can be applied fully self-consistently (two-component ZORA Hamiltonian) in both the molecular DFT code ADF and the periodic DFT code BAND.
Furthermore, SOC in ADF can be used for many spectroscopic properties (NMR, EPR, UV/ VIS, XAS) and one can calculate spin-orbit coupling matrix elements between excited states.
You can try out ADF & BAND (the whole ADF modeling suite) for 30 days from the SCM website through the link below.
Hope this helps, let me know if you have further questions