The answer is NO (as has already been said). The New York Times (and others including the venerable snopes website) have covered this myth. As stated in the NYT:
“This myth stems from the fact that turkey contains tryptophan, an amino acid found in proteins and essential to the human body. Scientific studies show that sleep and mood are affected by tryptophan.
However, turkey does not contain an exceptional amount of tryptophan. Chicken and beef contain about the same amount, and pork and cheese contain more tryptophan per gram than turkey. Because turkey is consumed with other foods, absorption of tryptophan from turkey is minimal, noted the authors. The myth likely stems from the fact that everyone feels drowsy after eating a large meal because the body is using energy to digest food and blood flow and oxygenation to the brain decreases. Large meals in the United States usually occur around Thanksgiving and Christmas, holidays during which turkey is often served.”