Record-wise it's the Texans but I'd give them a pass because they're still a very new team.
It's got to be the Cardinals. Been around for 90 years, worst winning percentage of anyone besides the Texans and the Bucs (who've only been around since 1976), made the playoffs eight times (but won two conference championships).
Falcons are really bad too but the Cards have been a team for a lot longer.