Can I eat wild carrots?

Well, yes, is the answer while not understanding the fascination with the wild carrot's smaller, paler, more fibrous roots. However that being said, you'd better not make a mistake in identification. Poison Hemlock (Conium maculatum), not the conifer, but the carrot-like weed of Socrates fame is very similar particularly in the juvenile 1st year stage when you would want to harvest the root. And if you do make this mistake, it could well be your last. At that stage the carrot foliage is hairy and the poison hemlock hairless, but do you want to bet your life on such a character? Here's an image of both; you decide which is which. The wild carrot has a pale yellow color to the root while that of poison hemlock is white. When mature they both have flat umbels of white flowers, and many people would think the poison hemlock a wild carrot, but the purple splotches on the stem and a rank odor to the foliage readily identify the poison hemlock except you don't harvest roots at this stage because this storage organ was used having provided the energy for flowering and fruiting. Stalk the wild carrot with care. You been warned.