Good observation. Upon investigation I've found it used by newsletters I'm subscribed to.
Join our free weekly newsletter
Looking at the definitions for join I don't see any way this usage of the term could be correct.
An alternative usage of join I have seen, that is correct is - "join the mailing list".
join (verb)
Become a member or employee of.
‘she joined the department last year’
Maybe arbitrarily swapping newsletter for mailing list is what leads to this error.
