As the U.S. moves into a new theater of the war on terror, it will miss its best chance to beat back Islamic State and other radical groups in the Middle East if it doesn’t deploy a crucial but little-used weapon: an aggressive agenda for economic empowerment. Right now, all we hear about are airstrikes and military maneuvers—which is to be expected when facing down thugs bent on mayhem and destruction.

But if the goal is not only to degrade what President Barack Obama rightly calls Islamic State’s “network of death” but...