  We propose that the superconducting pairing symmetry of organic
superconductors $\kappa$-(BEDT-TTF)$_{2}$X can be determined by measuring the
position in momentum space of the incommensurate peaks of the spin
susceptibility. We show that the positions of these peaks are uniquely
determined by the symmetry of the superconducting state and the geometry of
Fermi surface. Based on the effective Hubbard model on an anisotropic
triangular lattice, we demonstrate the different incommensurate patters of spin
responses for $d_{x^{2}-y^{2}}$- and $d_{xy}$-like pairing states. In addition,
we predict the nonexistence of the spin resonance mode in this compound, which
is an important feature in high-$T_{c}$ superconductors.
