Any program that can make a decision based on data is an AI. Bitcoin fits that definition.
That's a very loose definition of AI, and a far cry from the multi-layered convolutional neural networks that are used these days to do real machine learning. Bitcoin does make decisions based on data, but it cannot learn anything or change it's 'mind' in anyway because it's just a dumb algorithm.
I read a very interesting book a while back by Dr Roger Penrose called "The Emperors New Mind" in which he presented the evidence for his opinion that computers can never actually become conscious no matter how clever the algorithms they are running. I won't pretend I understood much of the mathematics or physics presented, but I believe I did grasp the main thrust of the argument that consciousness itself is not algorithmic in nature and computers can only ever be completely algorithmic.
Good read I recommend it.