You could try some of these ideas:

-tanglefoot, sticky stuff on a band of heavy paper wrapped around the trunk (or purchase the trunk banding paper I've seen at Fred Meyer on clearance lately) -- ants stick to it while trying to climb up trunk to get to figs

-metal flashing or something as slippery barrier or coat with petroleum jelly to prevent ants crossing over it

The ants might be going for aphids, so if you plant nasturtiums nearby they will attract the aphids instead of the fig tree.

Thx for the ideas; I'll follow up. This fig tree is planted against a storage shed, and my ant-less figs are out in the open. Guess I was thinking the ants might be leaping off the roof of the shed into the upper branches! Maybe hanging by their little antennae while scrambling for a foothold. So Tanglefoot sounds good to me.

Most likely the ants are nesting under the shed and climbing the handier nearby fig.