The social networking site had been threatened with steep fines if it did not comply with Judge Matthew Sciarrino Jr.'s order earlier this summer to turn over the records in the case of Malcolm Harris.
The tweets were handed over Friday.
The Manhattan district attorney's office says Harris' messages could show whether he was aware of the police orders he's charged with disregarding. The case involved a protest at the Brooklyn Bridge last fall.
Twitter had said the case could put it in the position of having to take on legal fights that users could otherwise conduct on their own.
Harris' trial begins in December. He has pleaded not guilty.