  CrX$_3$ (X = Cl, Br, I) have the same crystal structure and Hamiltonian but
different ligand spin-orbit coupling (SOC) constant $\lambda_X$, providing
excellent material platform exploring for exotic two-dimensional (2D) spin
orders. Their microscopic mechanism underlying 2D spin physics and Hamiltonian
remain unestablished, along with experimental corroboration of Kitaev exchange
interaction, central to realizing topological quantum spin liquids. We report
Kitaev interaction signature in magnetic anisotropy measured by ferromagnetic
resonance (FMR) spectroscopy. We present measured values of Heisenberg J,
Kitaev K, and off-diagonal symmetric $\Gamma$ exchange interactions in CrX$_3$
determined using FMR and exact diagonalization. K and $\Gamma$ exhibit dominant
quadratic dependencies on $\lambda_X$, indicating its central role in 2D
magnetism. Our study provides foundation for exploring exotic 2D magnetic
topologies by tuning intrinsic material parameters such as SOC.
