It's even Turing complete (not that a programming language needs to be)
It's just not a general purpose programming language like e.g. Python/C/Java/etc
Unlike it seems almost everyone else replying here, I'd say it is a query language and not a programming language.
Maybe an artificial distinction, but I don't think of SQL statements as programs.
The argument of “it’s a mark up language” tends to not hold weight for me as when I ask people why they say “because it’s in the name” - which, for me, misses that HTML is considerably more developed now than when it was named and should be measured on the current feature set.
It’s not a hill I’d want to die on though so really, it doesn’t matter.
That said, I think SQL, CSS and maybe HTML are the only ones that are a league of their own, that is, you could get a job as a pure CSS or SQL programmer.