More than likely a bird caused the initial fig damage and the ants moved in. Since these ants like "sweet" I'd place a few liquid terro traps at the base of the tree, once the queen is dead the ants will diminish in number in short order. By "traps" I mean use small bottle caps filled with terro for the ants to slurp up.

Try tanglefoot.

I too was thinking of tanglefoot but if Joe's fig tree is anything like mine then about a dozen or so limbs are coming up from the ground level which would be a job to tangle with. Killing the ants solves the problem easily and long term.....and of course the birds are another story.

Sprinkle the ground evenly with DE (Diotomacious Earth). The ants can't cross it without dying. DE isn't poisonous but is deadly for bugs of all kinds. I even sprinkled some on the lower parts of my Meyer Limon... just to make sure. You could sprinkle the ground under where the branches touch the ground and around the base of the tree.

Spray tanglefoot around the trunk of every trunk emerging from the ground. I tried DE and it did not work after rain. I put tanglefoot around the trunk of every okra plant I had and it kept the ants off and lasted all season.