Join our newsletter?

Is not the phrase 'Join our newsletter' wrong? Newsletter is a communication medium, right? Like a newspaper, or an email. So, it should ideally be 'subscribe to our newsletter' or 'sign up for our newsletter'?

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.