Gordon Galloway, of Cambuslang, South Lanarkshire, was acquitted after a trial at Glasgow Sheriff Court.
The trial had heard he posted the words "death... plain and simple" under a story about Mr McGrory representing IRA members during his time as a solicitor.
His defence lawyer said it was not a threat but a reply to another comment.
Speaking after the case, Mr Galloway's lawyer added: "His position throughout was that he accepted he sent the message but that it was misunderstood and not a death threat.
"The sheriff concluded in the end that she couldn't be satisfied that he'd meant to do that.
"She found that he sent the message, and he never denied it, but he didn't intend it to be a death threat, it's been misinterpreted."
He said the court case had put a "big strain" on his client.
"It's a serious charge which could've had serious repercussions for him, so he was relieved at the end of it."
A man from Scotland has been found not guilty of posting a death threat on Facebook to Northern Ireland's Director of Public Prosecutions Barra McGrory.