Shy Keenan, who founded The Phoenix Chief Advocates Consultancy, received 415 tweets in five months.
Penelope Mellor, 53, of Coven Mill Close, Coven, Wolverhampton, was convicted of aggravated stalking at Chelmsford Crown Court last month.
She was also given a 12-month community service order.
Ms Mellor was told to do 200 hours' unpaid work, pay £2,000 in costs within two months and pay a £60 victim surcharge.
During her trial, the prosecution said Mellor also sent material to Ms Keenan's associates and posted material online "which was considered unacceptable as criticism and personal in nature".
Simon Newell, senior prosecutor for the Crown Prosecution Service, said Mellor sent "insulting and abusive" publicly-visible comments to Ms Keenan's Twitter account.
She also emailed Ms Keenan's book publisher and literary agent, and sent messages to The Sun newspaper, for which Ms Keenan wrote a regular column.
"Ms Keenan was concerned private information about her family was being put into the public domain by Ms Mellor and threatening their safety, in particular, that it might be used by other people with grudges against her," he said.
Despite being warned by police about her behaviour, Mr Newell said, Mellor continued to send emails and mount attacks via Twitter.
A woman who stalked an anti-child abuse campaigner by "bombarding" her with Twitter messages has been given a restraining order for five years.