I think I have seen it spelled both ways.
Is one spelling more common or formal than the other ? (e.g. in the U.S.)
According to the New Oxford American Dictionary (that I have by default on my Mac :)):
The spellings adviser and advisor are both correct. Adviser is more common, but advisor is also widely used, especially in North America. Adviser may be seen as less formal, while advisor often suggests an official position.
Since it's an official position, I'd rather go for Ph.D. advisor