We don't know. Sirius correctly notes that all Wizarding families are related, so he is almost certainly related to every other non-Muggle-born in the series. Harry is therefore almost guaranteed to be related to Ginny, but only in the same way that all Britons are descendants of Charlemagne.
The furthest back in Harry's Wizarding blood we know about were his grandparents, Euphemia and Fleamont Potter, and his great-grandfather Henry Potter. Rowling never gives Euphemia and Henry's wife's maiden names, although both were presumably pure-blood witches since James was considered pure-blooded. So we know Harry's relations to fellow wizards could be relatively recent, but have no idea who they would be.
There is a Charlus Potter listed on the Black Family tree, who had a son with Dorea Black (1920-1977). Before Pottermore, people thought he was Harry's grandfather. If that had been true, Harry would be relatively closely related to Ginny, but Pottermore put a kibosh on that.
If Charlus only had a son, that would mean that the son and his grandchildren's last name would be Potter. Given the timeline, that would mean it's very, very unlikely that any living witches and wizards who are descendants of this branch of the Potters, since no one ever really mentions or brings up the Sacksville-Potters.
The absolute closest Harry could be related to another character is as a second cousin, if either Euphemia or Fleamont had siblings. So the good news is that at the very least, Harry's marriage is legal.