I need a thickening agent for tempura batter other than corn starch or regular flour. Help!

Arrowroot will work.

After this post I was thinking about tempura...and the Vodka based pie crust for making a light crust.
Turns out there are a few recipes that sub supercold vodka for the ice water for light crispy tempura.

Potato starch or rice flour.

You've tagged the question with gluten free.... But as far as I understand it, corn starch is gluten free. However, Ive seen rice flour in recipes for tempura, so you could try that?

any chance you have arrowroot or gluten-free-certified oats (which could be ground in a blender or processor?)

chickpea flour?