Reduce Subset-Sum to Sat
The Cook-Levin theorem demonstrates a reduction from SUBSET-SUM to SAT.
If you wanted a reduction from SAT to SUBSET-SUM, then yes, such a reduction exists; SUBSET-SUM is NP-complete, and thus the existence of such a reduction follows from the definition of NP-completeness.  You should be able to take any standard proof of NP-completeness for SUBSET-SUM and chain the reductions together to get the desired reduction.