The Rt Rev John Chalmers said the messages had come from "determined characters" on both sides of the debate over Scotland's future.
He made the revelation as he appealed for people on both sides to "turn down the volume on the rhetoric and refocus on the substance".
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His intervention comes days after it emerged author JK Rowling suffered a backlash on social media following her £1 million donation to the No campaign.
Mr Chalmers said: "This has not been a good week for those of us who promote Scotland's referendum debate as a 'respectful dialogue' - indeed the last few days have heard the siren voices of disrespect dominate the headlines.
"The General Assembly of the Church of Scotland held an extremely successful public dialogue on the independence question which I, as Moderator, chaired. I have found this public profile comes at a cost.
"If you take Twitter feeds or you have an accessible email address and people somehow think you might be influential - then you'll get messages that you would rather not receive.
"Apart from the distasteful remarks aimed at these who have donated big money to each of the campaigns, there are also other determined characters using dubious tactics to pressurise, rather than persuade, people over to their point of view.
"I've been the recipient of such messages - they have come from both sides of the campaign - and if I was at all a sensitive chiel I would think I was being bullied.
"Sometimes the writer purports to respect the fact that the Church of Scotland has declared its neutrality in the campaign, but they offer some other reason why it would be morally or theologically indefensible for me to maintain silence on one or another aspect of the public debate.
"I will not yield to their pressure and I have sincere hopes that no-one else bows to such offensive approaches."
But Mr Chalmers stressed it is important to keep a perspective on the issue, saying those acting in such a way are in a "tiny minority".
And for the most part, he argued, the public debate is being conducted at a very high standard.
He wrote: "I would be deeply distressed to find a 'dirty tricks' section at the heart of either campaign and while one or two individuals in the heat of the passions that are running high may have gone too far, I believe that both sides are trying to win the argument on principle and on substance.
"With less than a hundred days to go, however, it is a good time to turn down the volume on the rhetoric and refocus on the substance.
"Trading in personal insults will not win votes, bullies are no part of Scotland's future so we don't need to encourage them now and since we have to live with one another whatever the outcome we need to treat each other with respect now."
He added: "On September 19 there will be no 'them and us', only 'us', so now is the time to keep the dialogue respectful."