It's not the first time Trump has taken offence at SNL. Baldwin himself fired back, but so did Danielle Muscato, whose tweets went viral.
The transgender activist who describes herself as an atheist, civil rights activist, musician and trans woman, posted 30 tweets in succession. She advised the new leader of the free world to consider focusing on the important issues.
Each tweet was retweeted thousands of times. This is what she wrote.
The tweets continued. You can read them all here. But she ended with a promise.
"We will fight you every step, so be ready. You can't stop progress, no matter how hard you try."
In an interview with The Huffington Post, Muscato said she was "hardly alone" in feeling "terribly angry" at the election result.
"But amazingly, things are turning out to be worse than I imagined. Trump ran for the wrong reasons, namely, enriching himself," she said.
"He never wanted this job, and now that he has it, he's hoping a 'fake-it-til-you-make-it' approach will be sufficient for the most powerful office in the world. He's wrong, and it's repulsive."
It's yet to be seen how Trump will perform as president. One thing is almost certain - the running commentary will continue play out on Twitter, from both the President-elect and the public.