Yes, Korean food has gluten-free options! On the second day of the new year, we had dinner at Pyeongchang Tofu House in the Temescal neighborhood of Oakland California. The staff (ask for Tom) was attentive to our gluten-free needs.
In addition to the bi bin bop and selected soups (not all are G-F), the steamed pork (bo-ssam) with kimchi was excellent. Note that not all the banchans (appetizers) are G-F. The restaurant makes its own tofu, so try to the silky tofu soups.