Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain.
Reheat turkey stock in a separate pot over medium-low heat. Stir in gravy and soy sauce.
Combine 1/4 of the noodles, 1 1/2 cups broth mixture, and 1/2 cup chopped turkey in a bowl; repeat with remaining noodles, broth, and turkey.