Divvox2, I hate to tell you this but it is unfortunately likely true in this scenario: expect table variation.
My personal belief is that the rules on this are contradictory. If you look at the chart for animal item slots it has a column for "grasp". It says:
"Some creater body types are able to grasp and carry one object at a time in their paws, claws, or hands including weapons, rods, wands, and staves, though they may not be able to use such items effectively (GM's discretion) and take penalties for nonproficiency as usual."
So I disagree with claudekennilol that it is a straight out "no" in PFS. However, I think that at best something with a "GM's discretion") is going to be just that unless there is a specific PFS ruling.
I think the logical reading of those rules is to believe that with the proper Int and Proficiencies and Feats that your companion would be able to wield a weapon. Actually, I think I can remember some Paizo published material that had an Animal Companion using a weapon but I can't seem to remember where it was from.