The scare was started by conspiracy theorist Simon Parkes, an ex Whitby town councillor, who claims to have contacts on Capitol Hill.
He wrote two posts on his website about the alleged tweets from Mr Trump, who regularly uses the social network site.
Mr Parkes wrote: “President Trump tweets – ‘The time is upon us – operation Alice in Wonderland is about to start’.
“Clearly the president wishes to alert the people to some subterfuge about to take place.
“The tweet was swiftly removed around 15 minutes later.”
Two days later he updated hits claims, adding: “I was alerted by a contact in Capitol Hill.
“The tweet was taken down extremely quickly, I think by the President himself who thought better of it.
“The tweet was in reference to a planned psyops which would take the world into an Alice in Wonderland – nothing is real – set of happenings.
“My contact was of the opinion that by tweeting even if it was removed almost immediately that it might have prevented whatever it was.
“When I sought clarification I was told the tweet was removed in 15 seconds and not 15 minutes, that was my error.”
Psyops are defined as those to influence the emotions, aims, reasoning and behaviour of governments, organisations, or individuals through covert psychological means.
Conspiracy theorists claim future planned psyops will include so-called false flag events using holograms to trick us into believing aliens have landed to see how the public reacts.
The posts were quickly picked up by number of other conspiracy theory websites and YouTube channels, but none appeared to add any more detail, and most simply repeated Mr Parkes’ claims.
No screen shots have emerged of the alleged tweets, convincing many that Mr Parkes got it wrong.
Viewers of YouTube channel Lucid Dreamer were not convinced it happened.
James Garner posted: “Someone would have screen shot it. Not seeing one out there.”
Another with the user name Guts1 added: “I don’t believe this because I did not receive a tweet notification about it.
“So I would be able to see it on my phone even after it had been removed.”
Jon Watts wrote: “Why there is no other information on this anywhere on the net?”
The only other reference Express.co.uk found to Mr Trump and Alice in Wonderland was when Harry Potter author JK Rowling used the Lewis Carroll novel to attack him.
After Mr Trump tweeted about cancelling press briefings due to being unhappy with news coverage, Ms Rowling tweeted the famous quote from the book: “`I don’t think–’
“`Then you shouldn’t talk’, said the Hatter.”
Mr Parkes has made some outlandish claims in the past, including that in 2011 he stopped “Satanic scientists” from using the Large Hadron Collider to open a portal to bring the Devil to earth, by group meditation, as revealed by Express.co.uk.
He also claims on his website to be a “life long experiencer of aliens, shadow people, elementals and ufos”.
He claims many of his relatives have worked in the secret service and he also charges a fee to “read people’s souls”.