If recognizing oneself in a mirror is what interests you, then this robot has it.
If modeling oneself formally is what interests you, then a quined Lisp program has it.
If successfully pretending to be human, showing emotion, acting irrationally, winning at chess, is what interest you, then some of today's AIs have it.
First define what you are looking for in this context -- then check if an AI has it.
Apparently a PhD candidate at the Social Robotics Lab at Yale created a self-aware robot:
What do Less Wrongians think? Is this "cheating" traditional concepts of self-awareness, or is self-awareness "self-awareness" regardless of the path taken to get there?