For economists, a "cartel" refers to a group of firms jacking up prices to exploit consumers. Thus, I infer that this Arizona-based chain of coffee shops is not seeking the business of economists.
The company's website features comments like "WE ARE CARTEL" and "JOIN THE CARTEL." I know nothing about the company's thinking in using the term. I suppose the use of "cartel" may be an ironic comment on the really big coffee-store chains; or perhaps it just sounded cool; or perhaps the company is trying to emphasize the cooperative nature of what happens inside a cartel, while deemphasizing the costs imposed on everyone outside a cartel. But for an economist, telling a consumer to do business with a cartel is like telling the sheep that it's time for shearing.
Hat tip: Victor Claar spotted this store at the Phoenix Airport and posted this picture on Facebook.