The American version of the wild turkey was introduced to the early Pilgrim settlers by the native american Wampanoag tribe after the Pilgrims arrived in 1620.

The first year for the settlers was bleak, with many dying from the journey. That first winter, 46 of the original 102 Pilgrims died. Their seeds planted the next spring, aside from barley, did not produce any usable crops. The Wampanoag assisted the settlers, introducing them to native foods such as corn and squash and showed them how to hunt and fish. The first Thanksgiving was celebrated in 1621 at the request of Governor William Bradford, and the Wampanoag were invited guests of honor.

There is no specific mention of wild turkey in Edward Winslow's account of this first Thanksgiving but there was mention of "fowl" which most likely included wild ducks and turkeys. Edward Winslow wrote this in a letter dated December 12, 1621. The complete letter was first published in 1622.

Our corn [i.e. wheat] did prove well, and God be praised, we had a good increase of Indian corn, and our barley indifferent good, but our peas not worth the gathering, for we feared they were too late sown. They came up very well, and blossomed, but the sun parched them in the blossom. Our harvest being gotten in, our governor sent four men on fowling, that so we might after a special manner rejoice together after we had gathered the fruit of our labors. They four in one day killed as much fowl as, with a little help beside, served the company almost a week.....

The only other description of the "First Thanksgiving" was written about twenty years after the fact by William Bradford in his "History Of Plymouth Plantation". Bradford's "History" was rediscovered in 1854 after having been taken by British looters during the Revolutionary War. Its discovery prompted a greater American interest in the history of the Pilgrims. It is also in this account that the Thanksgiving turkey tradition is founded.

They began now to gather in the small harvest they had, and to fit up their houses and dwellings against winter, being all well recovered in health and strength and had all things in good plenty. For as some were thus employed in affairs abroad, others were exercising in fishing, about cod and bass and other fish, of which they took good store, of which every family had their portion. All the summer there was no want; and now began to come in store of fowl, as winter approached, of which this place did abound when they came first (but afterward decreased by degrees). And besides waterfowl there was great store of wild turkeys, of which they took many, besides venison, etc. Besides they had about a peck of meal a week to a person, or now since harvest, Indian corn to that proportion. Which made many afterwards write so largely of their plenty here to their friends in England, which were not feigned but true reports.

Conclusion -

Wild turkey were most likely served at the first Thanksgiving and remain a fixture in Thanksgiving menus to this day.