Using acupuncture to help animals is a relatively new field of veterinary medicine. In January, the American Veterinary Medical Association voted to admit the American Academy of Veterinary Acupuncture as a partner organization. Animal acupuncture has been practiced in the U.S. since the 1970s, the AVMA said, and began picking up steam in the 1990s.
As far as acupuncture's actual efficacy goes, the jury is still out. A summary of the medical literature in humans determined that "acupuncture is effective for some but not all types of pain." In domestic animals, too, results are unclear, with sparse evidence to recommend for or against the procedure. (But that hasn't stopped animals, like elephants in Maine, from receiving it.)
For this owl, the occasional pokes with small needles don't seem to be hurting. And as Cornejo noted, "It does not cause side-effects" like pharmaceuticals. But the few months of rest, plus a steady supply of fresh prey for the tiny predator, is probably helping out, too.