First off, what on earth does this phrase mean?
The most commonly used definition of crow’s-feet is “tiny wrinkles at the outer corner of the eyes, resulting from age or constant squinting” and are so called because of the likeness to a crow’s foot or footprint. It originates in the late 14th century from Middle English and is believed to have first appeared in print in Chaucer’s poem “Troilus and Criseyde.”
The phrase in the singular is crow’s-foot, but it is most often used in the plural, as in crow’s-feet.
“Hey, Buffy,” Xander said, squinting a little. “Did you know those wrinkles at the corners of your eyes kinda look like bird tracks?"
“What?” Eyes widening in horror, Buffy immediately reached up to touch the area in question. “Crow’s-feet? I’ve got crow’s-feet? I’m too young to have crow’s-feet!”
When Chris smiled, the corners of his eyes crinkled. But those crow’s-feet weren’t the product of age, as Ezra knew quite well: they were from peering into the dusty, sun-baked distance, searching for something more.
It can also mean “an embroidery stitch with three points, used as a finish at the end of a seam or opening,” or “an arrangement of ropes in which one main rope exerts pull at several points simultaneously through a group of smaller ropes, as in balloon or airship rigging.” These other definitions are much less frequently used, and when they are, it is usually in the singular crow’s-foot.
Willow examined the underside of the altar cloth and smiled when she saw that each of the hand-stitched seams ended in a flawless crow’s-foot. “You can always tell when your witchy accoutrements are made by someone who takes pride in her work.”
“That don’t look like any net I’ve ever seen,” Vin said, hunkering down next to Josiah to study the array of ropes.
“It’s not really a net,” Josiah replied, splicing another short length into place. “It’s a crow’s-foot, and it’s going to control that balloon when I finally get it to fly.”
Vin snorted. “If man were meant to fly, he’d have wings.”
Even though you might be tempted to put the apostrophe after the s – making it crows’-feet – the correct construction is crow’s-foot or crow’s-feet, including the hyphen. The crow does have two feet, after all.
Dictionary.com, here and here
Etymology Online, here