The gluten free menu is slim, but it's one of the few places with gluten free buns (Udi's).
Per their website (May 2019):
"*Culver's Restaurants are not gluten-free environments. While we take special precautions to prevent cross-contact, the possibility exists for food items to come in contact with other food products during preparation and cooking procedures. Please alert staff to your gluten-free needs."
However, they also note that the GF hamburger buns are warmed and served separately so it seems there would be a much lower chance of being accidentally glutened.
No