Probably not much, as Brad Jones learned over Easter when a neighbor allegedly blasted his DJI Phantom. Even if his prime suspect confessed, there's not much precedent for prosecutions.
The Federal Aviation Administration considers it akin to shooting at any aircraft, but there have been no federal prosecutions for drone-blasters, according to Ars Technica:
While some on the ground may feel that their "airspace" has been invaded if a drone flies in or near their property, American law does not yet recognize the concept of aerial trespass. In fact, as the consumer drone age has taken flight, legal scholars have wondered about this exact situation. If a drone flies over private property, is it trespassing?
The short answer is that American courts have not addressed the question adequately. The best case law on the issue dates back to 1946, long before inexpensive consumer drones were technically feasible. That year, the Supreme Court ruled in a case known as United States v. Causby that a farmer in North Carolina could assert property rights up to at least 83 feet in the air, and perhaps further. But he could not assert property rights indefinitely.
As the Supreme Court ruled at the time: "We need not determine at this time what those precise limits are."
The punishment for deliberately hooking a drone appears to be making the hooker a viral sensation.
• Man takes drone out for a sunset flight, drone gets shot down (Ars Technica)