No.

Statute 33-6-107(9) and Wildlife Commission Regulations (WCR) 312(C), WCR 323, WCR 1000(A)(6), WCR 17122(C), WCR 17123(A) & WCR 17141(A)
If wildlife is causing damage to crops, real or personal property, or livestock - a person (or any employee or agent of the landowner) may hunt, trap, or take the following wildlife on lands owned or leased by the person without securing a license to do so:
Black-billed magpies, common crows, starlings, English or house sparrows, common pigeons, coyotes, bobcats, red foxes, raccoons, jackrabbits, badgers, marmots, prairie dogs, pocket gophers, Richardson's ground squirrels, rock squirrels, thirteen-lined ground squirrel, porcupines, crayfish, tiger salamanders, muskrats, beavers, exotic wildlife, and common snapping turtles.