Luffy, the main character of the anime/manga series One Piece, is not related to Gol D. Roger, the former Pirate King. While both characters share the dream of becoming the Pirate King, they have no known familial connection.
Roger was executed by the World Government for his crimes as a pirate, while Luffy currently remains at large (although he is technically a wanted man as well). However, even if they were related, it's doubtful that Luffy would be welcomed into Roger's family with open arms given his current situation.
So while there may be some similarities between the two characters, they are not actually related.