John McCabe, 54, posted the threat to SNP politician Dr Lisa Cameron because he felt she had failed to help him in relation to an inquiry into historic child sex abuse.
She called in police and was left so distressed by the incident that she has had to seek counselling.
McCabe, of East Kilbride, Lanarkshire, claims he was sexually abused for six months when aged 17 at HMP Medomsley Detention Centre in County Durham and has called for a public inquiry into the institution.
Dr Cameron, his constituency MP, had wrote to the UK government on his behalf but told him last year that she could not take the matter any further.
But when she tried to sever ties with him, he posted a photo of her which suggested she posed a threat to children and was ignoring abuse claims.
In the post, which was sent during the SNP conference, he wrote: “SNP conference urged to reform sex education in wake of MeToo. @DrLisaCameronMP was made aware at a meeting of the sexual exploitation and sexual abuse rife in her constituency.
“Dr of child sex abuse. Cameron MP. Her parliamentary salary is her quest. An incredible threat to children.”
McCabe, of East Kilbride, appeared at Hamilton Sheriff Court and admitted posting the threatening message in October last year.
Prosecutors have now asked for him to be banned from contacting her.
Depute fiscal Wendy McAdam told the court: “The complainer first had dealings with the accused two or three years ago and she was writing to the UK government on his behalf.
“However, according to the complainer, Mr McCabe did not get the response he wanted and was probably blaming her.
“A letter was sent to him two years ago about the issue he wanted addressed.
“Further to that, six months ago Mr McCabe emailed the complainer regarding the outcome and at this time, the complainer emailed Mr McCabe to say that the situation was at an end and if he wanted to do anything he would have to go to another MP as she didn’t want to deal with him.
“On the back of this he posted an entry on the complainer’s Twitter page along with a photo of her. This came to light when her husband decided to have a look at his wife’s Twitter.
“When he phoned his wife to tell her she was immediately alarmed because of the fact she is a public figure and contacted the police.
“She told police that the post insinuated that she was some sort of child abuser and an incredible threat to children and this could insight others to cause her harm.
“The post has had adverse effects on her, she is a mother with young children and as a result of this she had to seek counselling.
“Hopefully the accused will know that she does not want to deal with him in the future and I move for a non-harassment order.”
Marco Guarino, defending, said: “Dr Lisa Cameron is a highly experienced child psychologist and is well versed in historical child sexual abuse and I say with a great deal of scepticism that she has needed counselling because of this.
“He felt he had been let down and that is why, in a moment of distress, he made the post and for that he apologies to Lisa Cameron for the alarm that caused her.
“It was not his intention to do anything other than highlight the lip-service the SNP were making to matters and that, having been approached by them and not the other way round, felt rightly or wrongly, that he had been a pawn in some sort of political move.
“He is now in contact with another MP about the inquiry and will be meeting with the Home Secretary so this is rightly being heard in the highest corridors of power in this country.”
Sheriff Alasdair MacFadyen deferred sentence on McCabe until next month for reports and continued bail.
He added: “You have pled guilty to a serious matter and you have accepted fear and alarm was caused by the posting of this on Twitter.
“You brought that into the public domain and it was brought to the attention of Dr Lisa Cameron MP.”
Dr Cameron qualified as a clinical psychologist before being elected to Westminster in the 2015 General Election as the MP for East Kilbride, Strathaven and Lesmahagow.
She took the seat from Scottish Labour for the first time since 1974 with a majority of more than 16,000.
In the 2017 General Election, she was re-elected but with a reduced majority of 3,866.