A microscopic theory of optical rotation in terms of the linear response theory is developed. The gauge invariance of optical rotatory strength is discussed. The general theory is applied to the long helical polymer by using the exciton model. It is shown that the result obtained by Moffitt, Fitz and Kirkwood may be derived under the assumption of the periodic boundary condition. When the helical axis of the polymer is parallel to the direction of incident beam, the rotational strength is shown to be independent of the helical radius of the polymer. Effect of the Umklapp process is evaluated.