Yes, if you choose the right brand. Before we continue, remember that barley is the most common bad-boy in beer. There are many brands of wheat-free beer available.
Read this article which gives information about thirteen brands of gluten free beer, and/or this one which talks about seven brands. The situation is not as good as the last sentence suggests — only Redbridge beer is available nationally and some of the beers are discussed in all three articles. However, the situation is definitely not hopeless.
My favorite among these beers is the brew from St Peter’s Brewery in the United Kingdom. I also drink Redbridge occasionally because it is available almost anywhere, reasonably inexpensive, and proof that celiacs can do anything that anyone else can — we just need to be more resourceful.
It is possible to brew your own gluten free beer, but the writer of the article includes the phrase “Should you try it?” in the title. I know I don’t intend to try, for cross-contamination reasons if for nothing else.