why yes you can! Found this on Epicurious!
Yes, watch out,
Punxsutawney Phil, apparently you and your kind are pretty tasty as well as darn cute and cuddly. No wonder you have that security detail with you at all times.
"The simple fact is, groundhogs are eminently edible and delicious," writes Everett J. Castro in Mother Earth News. "Like rabbits and squirrels (both of which are valued food animals), whistle-pigs are vegetarians. Thus, their meat, when properly prepared, is quite tasty and tender."
Castro gives recipes for his traditional Groundhog Day pie and also a hearty stew. "You can use woodchuck meat in virtually any recipe calling for small game and in many other dishes as well," he says