He doesn't have one. The Link from Majora's Mask is the same Link from Ocarina of Time. He travels to Termina, the land where Majora's Mask is set, unexpectedly. His house would be in his home land of Hyrule which is not assessable in Majora's Mask. Link can however take up accommodation in a room in the Stock Pot in by talking to Anju on the first day.
In addition to the inn, Romania gladly offers Link a place to live at the ranch after he helps her fend Them off, in hopes that he can help her again next year. This doesn't really end up happening though, so it's likely she forgot.