The Wall Street Journal reports that a lawyer for the company announced the decision to appeal on Twitter on Thursday.
Lawyer Benjamin Lee said the ruling "doesn't strike the right balance between the rights of users and the interests of law enforcement."
The tweets are expected be used against Malcolm Harris.
He was among 700 people arrested on disorderly conduct charges during an Oct. 1 Occupy march on the Brooklyn Bridge. The case has evolved into a closely watched legal tussle over law enforcement agencies' access to material posted on social networks.
Harris' attorney said he was pleased with Twitter's decision to appeal.
The Manhattan DA declined to comment.