"You had one job, booker! One job!"
Again - SPOILERS
So, Booker sold his kid. Which is tragic - and hilarious. Let's just say he's a long way away from a "world's greatest dad" mug.
And seeing as there are a thousand realities in which Anna was carried off to Columbia, there are like a thousand possibilities of what happened. And one of those HAS to be that he got drunk and just accidentally sold her.
I am sure of this fact.
All characters are belong to the Bioshock Inifnite creators.