Whether SQL is a programming language or not is a fairly loaded question. What can be said about SQL is that it is a language and vocabulary users leverage to communicate with their computers to accomplish specific tasks. While these tasks aren’t as broad as general programming principles, they do correspond to a particular demand.
With this in mind, SQL is functionally a programming language. Some could argue that it is not Turing complete, but SQL has a specific intended purpose. Whether you consider it a programming language or not will boil down to which definition you choose to apply to programming.