AKCAKALE, Turkey—A quick and successful offensive by Kurdish fighters and allied rebels in a northern Syrian town has boosted a U.S.-backed effort to choke off Islamic State’s supply routes. Emboldened by this week’s recapture of Tal Abyad on the Turkish border, Syrian Kurdish fighters and allied rebels said their next target is Raqqa, Islamic State’s main stronghold about 50 miles south of Tal Abyad. On Monday, these fighters said they had already begun to advance southward toward Raqqa, reaching the town of Ain Issa, only about 30 miles away. “Now that we have just completed clearing Tal Abyad and the...