I found two scientific evaluations on the use of fig sap to heal warts. Both used control (no treatment) groups, which is standard practice in medical research.
The first study is on humans: "Comparative study of fig tree efficacy in the treatment of common warts (Verruca vulgaris) vs. cryotherapy."
The second is on cows: "Therapeutic effects of fig tree latex on bovine papillomatosis."
Both studies reported that fig sap was a successful treatment for warts.