Do you ever "download" a language?
A programming language is a formal language, informally speaking a collection of words with a well-formed set of specific rules. As such, you can write down the definition of a formal language and thus a programming language on a piece of paper. 

Also, if I've written down somehow digitally the definition of a programming language, surely you can represent and download that description. So then you might talk about an interpreter or a compiler for a language. That is not a programming language, that's an interpreter or a compiler. It's a program you might download.

If the question is "does a programming language exist outside of its description", the answer is no with the above definition: a programming language is defined by a formal language.