Heat oil in a large pot over medium heat. Add celery, carrots, onion, parsley, and bay leaf; cook until vegetables are tender, about 10 minutes. Add beef stock, chicken stock, turkey, salt, and black pepper; bring to a boil. Reduce heat, cover pot, and simmer until soup is heated through, about 15 minutes.

Stir rotini into soup; cook until pasta is tender yet firm to the bite, about 15 minutes.