  Motivated by the recent experiments on the triangular lattice spin liquid
YbMgGaO$_4$, we explore the effect of spin-orbit coupling on the effective-spin
correlation of the Yb local moments. We point out the anisotropic interaction
between the effective-spins on the nearest neighbor bonds is sufficient to
reproduce the spin-wave dispersion of the fully polarized state in the presence
of strong magnetic field normal to the triangular plane. We further evaluate
the effective-spin correlation within the mean-field spherical approximation.
We explicitly demonstrate that, the nearest-neighbor anisotropic effective-spin
interaction, originating from the strong spin-orbit coupling, enhances the
effective-spin correlation at the M points in the Brillouin zone. We identify
these results as the strong evidence for the anisotropic interaction and the
strong spin-orbit coupling in YbMgGaO$_4$.
