It is permissible
to swear by Allah, His Attributes, and the Qur'an which is the Word of Allah and one of His Attributes. Therefore, it is permissible to swear by it if someone intends by swearing the Words contained therein. However, if they intend to swear by the papers of the Mus-haf and the ink, then it is not permissible, because papers and ink are created objects and it is not permissible to swear by created objects. The Prophet (Part No. 1; Page No. 355) (peace be upon him) said:
Whoever has to take an oath should swear by Allah or remain silent. (i.e. He should not swear by other than Allah.)
.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.