Yes Campbell's Cheddar Soup is gluten free.
Most if not all of Campbell's Soups and foods are gluten free including the Campbell's Cheddar Soup.
I have a gluten intolerance and can eat all of Campbell's Soups as well as the Campbell's Cheddar Soup and I never get stomach issues from it.
Most canned food is gluten free but some foods can contain gluten.
Some of the cans and food products will say whether or not they are gluten free but sometimes they do not.
Just like some noodles may contain gluten some other noodles do not contain gluten.
For example I can eat spaghetti that is in cans but not the spaghetti from a package that I make.