On Monday, a magistrate in Charlottesville issued a warrant charging Harris with unlawful wounding in the violence at the parking garage.
A third man was arrested in connection to the beating on Wednesday.
Harris' attorney has said that Harris did nothing wrong and that authorities don't have probable cause to charge him.
Harris, a former special education instructional assistant who sustained a spinal injury and head wound that required 10 stitches, was released on a bond after turning himself in to Charlottesville police.
Two men were charged with malicious wounding in September in the attack against Harris.
Warrants had been issued earlier this week for Harris, witched stemmed from an altercation on the day of the Unite the Right rally at the Market St. parking garage in Charlottesville. Harold Ray Crews, who identifies himself online as an attorney and "Southern Nationalist", has alleged that Harris injured him during the brawl.
Video of the incident appears to show a scuffle between the two in which Mr Harris swings a torch at a man identified by United States media as Mr Crews, who lunges at him with the pole of a Confederate flag.
Charlottesville Police say a wanted man turned himself in Thursday morning.
In the USA, alleged crime victims can go to a magistrate after filing police reports.
Harris's case is scheduled for a court hearing Friday morning at Charlottesville General District Court.
A counter-protester, Heather Heyer, 32, was killed when a driver ploughed a vehicle into a crowd.