There's a couple things that could be causing this. You changed the bulb, so it's not that. It is possible that the socket itself is junk. You can get one off rockauto.com for five bucks or so. Did you make sure that the socket itself is plugged into the harness correctly/completely?
Something worth trying first is contact cleaner. You can get this at computer stores, music stores, Hardware stores I believe; fairly common. Soak the socket and plug with that and see where that gets you before you start throwing parts at it.
If that doesn't work, get a test light. Clip one side to the body or the negative battery terminal and activate the turn signal. See if you get power at the harness. If there's no power then replacing the socket won't do you any good.
Although it's a longshot, see if the problem changes with your tilt column being up or being down. My father's 03 Ranger Edge had a right turn signal problem as well, and it turned out to be the multifunction switch's harness that was faulty.
Give those things a try and see where that gets you.