Certified GKH Gardening Expert
Fig rust is sometimes curable but will sometimes come back no matter what you do (especially if there are other fig trees near you that can spread the disease back to your fig).
The most important step is to remove all the diseased leaves as soon as the signs of rust show up. Also remove any fallen leaves or debris beneath the tree, since they could serve as a hiding place for the fungus. Tie the diseased parts up securely in two plastic bags and discard. Try to keep the fig's foliage dry as much as possible because moisture promotes the disease.
If available in your area, copper fungicides have been reported to help. This article has more advice: