Recruiting an arcanist will allow the Inquisition to craft runes to enhance weapons and armor.
Recruit an arcanist at the war table by completing the operation Acquire the Arcanist then head to the Undercroft where you will be introduced to the new recruit through a cutscene. You are granted the Corrupting Rune Schematic at this point and are prompted to craft a rune to progress the quest.
Simply click on the Craft Weapons station to complete the quest. You don't actually need to craft a rune for the quest to complete.