Roadkill, a short story by Mercedes Lackey. I'm very nearly certain. I found it in the anthology, Werehunter (published 1999), but it was published summer 1990 in Marion Zimmer Bradley's Fantasy Magazine, which can fit your timeline. It isn't the first story in the anthology, but it is nearly the last, if that helps - and the anthology has a short blurb at the bottom of each story, about the next story in the anthlogy (so there is a short blurb about "Roadkill", about where the idea came from, on the bottom of the previous story, "Stolen Silver").
In the story, the main character is in the habit of making mental calculations about things as they cross his path - this leads him to notice something that looked like a flattened cardboard box, when it seemed to skitter out of the way of a jerkish driver, against the wind. Later he notices the roadkill the box had come to rest against had vanished.
He recalls some memories of stories, about a shape-shifter that would scavenge food by pretending to be inanimate objects (for example, a carry sack which people would place food into, which would then walk off with their hunt when they weren't looking). He thinks about how such a creature could survive the changing world, full of people that it doesn't know how to fool, and thinks about the amount of roadkill that might entice such a shapeshifter to look like trash, instead of actively tricking people (who don't believe in magic, or may react very badly to such tricks).
And in the end, he does go back, finds the box, and deliberately aims his car at it to prove is is a similar sort of creature, or else prove it's just a box. The story ends with the creature leaping onto the windshield, where he sees its flattened face (and huge, chisel-like teeth), and the car going out of control because it had bitten through his brake lines.