Rule As Tweeted (RAT) is ironically used when a tweet from a the game designers contradicts RAW (rules as written) or (perceived) RAI (rules as intended).

Who used it first? Did it originate here on RPG.SE?

It's more like a recurring joke than an actual term and its origin is unclear

There appear to be smatterings of the term across Giant in the Playground (example) and Reddit (example) around 2015/2016 that arose to categorize in a joking and derogatory manner the rulings of D&D 5e Lead Rules Developer Jeremy Crawford which he often makes on Twitter.

The first mention of it on RPG.se that I can find is this answer from 2016. It reemerged in late 2018 in an answer here and a (now-deleted) derisive 2019 comment on this question (which seems to have been the impetus for this question). It is unclear if the later answer was referencing the older answer or came to the same joke independently a few years after the fact.

In fact, it is unclear if the term actually "originated" anywhere or if people on different forums and communities are simply coming to the same joke independent of each other (or unconscious of the previous usages). After all it is a really easy jump from RAW/RAI and people play around with those terms a lot in joking ways.

At this point, it doesn't seem to be used enough to even really deserve the honor of being considered a term. More like an occasionally recurring joke.

This is a joke/derogatory term, is redundant and not useful, and using it in a real capacity should be discouraged

We already have enough "Rules as..." terminology and they already cause quite a bit of confusion both among new and experienced users. The fact is, RAT is not a useful designation. All of Crawford's tweets already fall under either his opinion/interpretation of RAW (rules as written)¹ or RAI (rules as intended) and occasionally RAF (rules as fun). Each of these terms have formal definitions and accepted community usage and, more importantly, make useful distinctions between different types of rules analysis. Lumping all tweets together as RAT tells us nothing about the type of analysis being done and actively removes all the clarity and meaning of the other terms. The only thing it adds is a joking derisive tone.

A much better way to handle critiquing rulings would be to correctly (to the best of one's ability since Crawford often doesn't make it easy to distinguish) identify the type of ruling Crawford was trying to make (RAW/RAI/RAF) and then state how it disagrees with the rules/common sense/is otherwise undesirable or bad in your view (and backing it up with the proper support of course).

^{1 - These can be very tricky distinctions, but it is important to note that JC tweets are never considered to be RAW themselves, though they might oftentimes offer up an interpretation of what RAW is (much like answers here do). Crawford's tweets are also not all RAI (by his explicit definition). I recommend reading this Q&A and Q&A for more on this train of thought since it is beyond the scope of this question.}