Umm...
Annie as tank?
Just for fun I tried playing Annie as a tank.
To my surprise I found out this is EPIC.
Everyone expects Annie to be an easy kill.
Being targeted and surviving while Tibbers keeps attacking is brilliant.
Annies molten shield benefits really well with tank gear.
This is the build I use

Well I mostly play my regular AP rune set,
3 movement quints, magic resist glyphs,
mana reg seals and magic penetration marks.

Like most tank builds I use 0/21/9

I start of with a regrowth pendant and a health potion.
Now I can stay in the lane much longer due to the hp reg.
First back I pick up Ruby crystal or Giants belt, depending on how much money I have.
Since I have my movement quints I usually buy boots very late in the game.
If you feel the need you could pick up some boots.
The goal is to rush a Warmog's ASAP.
Last hitting with Annie is easy thanks to Disintegrate.

Depending on the other team I choose to build either force of nature
or thorn mail. My games usually ends by now, if the is not yet finished
I buy a Rylai's for the health and to actually get some AP.
If the game is still going on I buy a Rabadon's.
Do not mess with Tankie after this...

When I feel I got some money over or become tired of being slow I
buy boots. Boots > Mercury Threads.

Begin with Incinerate.
Fast early game stun is very handy.
I then go for Disintegrate.
Now I should be able to last hit very well.
Next up is Molten shield.
I then switch between leveling Disintegrate and Molten shield
and ofc Tibbers when available.