Should be called...
...Resident Evil: Bioshock. It certainly manages to get the same atmosphere as Rapture.
Okay, so there's no plasmids, but I am relating specifically to the mood, presentation and even the boss fights: Jack is like Steinman, Marguerite is like a spider splicer, the trials with Lucas are like the mission set by Cohen.
They even have a Big Daddy!
Welcome to Rapture / the family son.