Here’s an excerpt from William Dembski’s Design Inference:
… suppose I walk down a dirt road and find some stones lying about. The configuration of stones says nothing to me. Given my background knowledge I can discover no pattern in this configuration that I could have formulated on my own without actually seeing the stones lying about as they do. I cannot detach the pattern of stones from the configuration they assume. I therefore have no reason to attribute the configuration to anything other than chance. But suppose next an astronomer travels this same road and looks at the same stones only to find that the configuration precisely matches some highly complex constellation. Given the astronomer’s background knowledge, this pattern now becomes detachable. The astronomer will therefore have grounds for thinking that the stones were intentionally arranged to match the constellation. (p.17)
I think Dembski would also say fairy rings are specified: its specification is a circle.
The last question is whether the fairy ring is complex, because his design inference has two criteria: specificity and complexity. Dembski says something is complex if it has a low probability. Low probability would be relative to our background knowledge. For pre-scientific people, this circle could be interpreted as having low probability. In fact, fairy rings have been associated with fairies, witches, demons, dragons, etc.
Dembski claims his design inference yields no false positives. Well, why wouldn’t this be one?
Dembski, William. The Design Inference.