"There's [a] person I know in a senior position at News UK who tells me they know RM is often drunk when he tweets," he wrote, referring to the British subsidiary of Mr Murdoch's News Corp which publishes The Sun, The Times and The Sunday Times.
Read more: 'The Sun' scrap its topless Page 3 girls? Have we all been had?
Mr Murdoch's message also attracted the attention of Graham Linehan, the Irish comedy writer and prolific Twitter user, who jokingly speculated that the media tycoon may be in his death throes.
Responding to Mr Linehan, the same user repeated his claim. "RM's often shitfaced pissed when tweeting and the editorial staff worry," he wrote.
The series of tweets by Mr Rooney, who deleted his account shortly after publishing the claims, prompted the US website Gawker to investigate further.
It ran the results under an article headed "Is Rupert Murdoch tweeting while drunk?"
The website said it had pieced together an online trail linking Mr Rooney to a top executive at The Sun.
According to his previous interactions on Twitter, Mr Rooney regularly took part in a quiz at the Prospect of Whitby pub in Wapping, east London, near to the former offices of Mr Murdoch's British titles, with people who knew the executive.
News UK declined to comment when contacted by The Independent yesterday, but Mr Murdoch himself appears to be aware of the allegations, as a scoffing tweet he sent out shortly after the claims were published clearly demonstrated.
"Believe Gawker, believe any nonsense," it read.
It is not the first time that one of Mr Murdoch's tweets has caused controversy.
Shortly after the Charlie Hebdo attack in Paris, he wrote that while "most Muslims" might be peaceful, they must ultimately be held responsible for the religion's "growing jihadist cancer".
His comments were widely condemned, prompting him to issue a clarification four days later.
"Certainly did not mean all Muslims responsible for Paris attack. But Muslim community must debate and confront extremism," he wrote.
Earlier this month, he angered anti-Page 3 campaigners by suggesting that the only people protesting about The Sun's pictures of topless women were "horrible elites".
One user who angrily responded was a nurse affected by the public-sector pay freeze.
Yesterday, Mr Murdoch called for Australian Prime Minister Tony Abbott's chief of staff to resign or be sacked, apparently in response to controversy over Mr Abbott's decision to bestow a knighthood on gaffe-prone Prince Philip.
But many of Mr Murdoch's tweets are more confusing than controversial.
In 2012, he sent out a message which simply read: "Louise Mensch."
He did not elaborate on why he had chosen to invoke the name of the British politician, who was then Conservative MP for Corby.
Mogul's missives: Murdoch's best tweets
June 15, 2012: I stand by every word is aid at Leveson.
July 12, 2012: What was wrong with Iraq war? Saddam Hussein evil major killer, etc. Execution another matter... Afghan bad every way now.
March 30, 2013: James
October 13, 2013: "Please expose Eric Schmidt, Google" etc. Just wait!
October 14, 2013: Oops! Better ignore last tweet.
February 9, 2014: Great partnership between spotify and Times of London. Fabulous tone quality. I link spotify to my jambox.
February 18, 2014: Wild winter in US, UK, etc. no respectable evidence any of this man made climate change in spite of blindly ignorant politicians.
April 13, 2014: Vegans wake up! Bill Clinton looks incredibly healthy after giving up this nonsense. We all need a little red meat.
April 20, 2014: Google grows more exciting. Now hiring top academics to work on anti-aging
July 28, 2014: Asked is my daughter friend of David Cameron? Don't know, but hope not. Really not my business.
September 10, 2014: Piers Morgan seems unemployed after failing to attract any audience in US. Seemed out of place. Once talented, now safe to ignore.
September 10, 2014: Did not mean to hurt Piers Morgan. Piers a friend and a legend.
November 29, 2014: Moses film attacked on Twitter for all white cast. Since when are Egyptians not white? All I know are.
January 10, 2015: Maybe most Moslems peaceful, but until they recognize and destroy their growing jihadist cancer they must be held responsible.
January 14: Certainly did not mean all Muslims responsible for Paris attack. But Muslim community must debate and confront extremism.
January 24: Much fuss and publicity in UK as horrible elites yak on about Page 3. Worry not, The Sun will always have great looking women - and men!
January 26: Po
- Independent
