According to this question and its answers, linguistics primarily focuses on spoken language and not written language.
This answer to another question indicates that this focus is a matter of historical trends and convention (i.e. linguists have chosen to focus their field on naturally occurring, human language and not on other forms of communication).
That being said, one of the comments on the first question says,
Linguistics may "focus" on spoken language (for reasons outlined by other people here), but that doesn't mean that written language is uninteresting or that it doesn't get studied at all. To my knowledge, text messaging e.g. has been extensively studied.
I am personally fascinated by text-based communication, and there are many questions that I think are interesting and potentially worthy of research (for example: how texting language differs from spoken language, how text based language has evolved with the internet, the presence of ambiguity in text-based language, the use of emojis vs words, etc).
If I wanted to research such questions, does it make sense to become a linguist? Is there an established sub-field of linguistics that focuses on written communication? Or would I find myself unable to research/publish on these questions because they fall outside of linguistics?
(Note: I'm also interested in spoken language and linguistics in general, so I think I would have no issue learning all about spoken language on my way to becoming a linguist. I'm just wondering whether that path makes sense at all if my goal is to research text-based communication)