Christopher Stevenson, 26, posted: "Think I might assassinate Alex Salmond" while watching a TV programme about him.
But an American visitor to Scotland saw the message on the social networking site and contacted the police.
Fire safety security technician Stevenson, from Alexandra Gate in Glasgow's east end, told police it was a joke when they interviewed him before he was arrested.
Stevenson, who has no previous convictions, was found guilty by Sheriff Graeme Warner after trial at Glasgow Sheriff Court of behaving in a "threatening or abusive manner which was likely to cause a reasonable person to suffer fear or alarm".
He told Stevenson: "I'm sure you must know we live in a fairly sensitive age when some people, typically young men do some pretty crazy things that older folk like me find almost impossible to comprehend."
The sheriff said although he accepted Stevenson meant it as a joke, had he been a Twitter user and seen the message he would have "opened his eyes".
He added: "I might even have gone so far as to contact the police - it wasn't a surprise to me in the least someone took that course of action."
The sheriff deferred sentence for a year for Stevenson to be of good behaviour.