Update: This article mentions a tug.
I'm not certain. IANAS(ailor) but I believe it could technically do either. This brief Reddit discussion backs that up a little, but it's never been officially answered to my knowledge.
This SFI article goes into some detail about the ASDS, including some information about the company supplying the dynamic positioning system: Thrustmaster's Portable Dynamic Positioning System. All of the press releases, Twitter mentions, and publicly-available info on the ASDS have discussed the fact that it can maintain position autonomously, but not how it gets to that position exactly. Of the two problems, maintaining a position is by far harder than moving to one.
An additional consideration is the question of what they are planning to do once the stage is secured. If they are keeping the stage on the barge and then moving everything back to shore, a tugboat may make more sense because there is additional weight involved. But again, my knowledge of boats > my knowledge of spacecraft.
Tl;dr - I think it will probably be towed by a tugboat because that's usually how barges move, but I'm not certain.