  Starting from a two-orbital model and based on the random phase
approximation, spin excitations in the superconducting state of the newly
discovered BiS$_2$ superconductors with three possible pairing symmetries are
studied theoretically. We show that spin response is uniquely determined by the
pairing symmetry. Possible spin resonance excitations might occur for the
d-wave symmetry at an incommensurate momentum about $(0.7\pi,0.7\pi)$. For the
p-wave symmetry the transverse spin excitation near $(0,0)$ is enhanced. For
the s-wave pairing symmetry there is no spin resonance signature. These
distinct features may be used for probing or determining the pairing symmetry
in this newly discovered compound.
