The billionaire demanded to know what pressure the First Minister exerted to get several organisations to withdraw their objections to the 11-turbine European Offshore Wind Development Centre (EOWDC) off the Aberdeenshire coast.
It came after an approach from one of Mr Salmond's senior advisors was revealed over the Lockerbie release. Mr Trump was asked to back the Government's release of the man convicted of the Lockerbie bombing, Abdelbaset Ali Mohmed al Megrahi.
He said: "Salmond put a great deal of pressure on me and my organisation to sign a letter dictated by him on Scottish Government letterhead, to fully endorse his absolutely disgusting decision.
"I am sure the same pressure that Salmond put on the Trump Organisation to support the horrible act was also put on the MoD, RSPB, Scottish National Heritage, the aviation authorities and others demanding that they drop their strong opposition and insurmountable objections to the ugly, inefficient, Chinese-made wind turbines that will litter the North Sea and almost all other parts of Scotland."
He said Mr Salmond should be investigated to find out how much pressure he put on "all of the above agencies and their administrators" in order to change their strong opposition to the EOWDC application. "In doing the investigation, all of the people from the respective organisations should be made to testify under oath and produce letters, emails etc."
A spokesman for the First Minister said: "Anybody reading this latest contribution from Mr Trump would have to agree his comments are becoming ever more ridiculous and removed from reality."
l The controversial film on the history of Mr Trump's golf development at Menie,You've Been Trumped, by Anthony Baxter, is to be screened on BBC2 on October 21.