This Peanut Dipping Sauce thickens as it sits, so all you have to do is wait! But seriously, the most obvious way to thicken peanut sauce is by adding more peanut butter, or less liquid.  However, if you don't want to alter the original flavor by messing with the ingredient ratios, use tapioca instead. Just mix the tapioca with boiling water to dissolve it. Then stir into the peanut sauce to thicken.