  In this paper, we derive a function field version of the Waldspurger formula
for the central critical values of the Rankin-Selberg L-functions. This formula
states that the central critical L-values in question can be expressed as the
"ratio" of the global toric period integral to the product of the local toric
period integrals. Consequently, this result provides a necessary and sufficient
criterion for the non-vanishing of these central critical L-values, and
supports the Gross-Prasad conjecture for $SO(3)$ over function fields.
