Fiqh-us-Sunnah Volume 5, Hajj and ‘Umrah, Fiqh 5.071.

A person may recite the Qur’an while performing tawaf, because the purpose of tawaf is to remember Allah and the Qur’an is a reminder and a remembrance of Allah. ‘Aishah reported that the Prophet (peace be upon him) said: “Tawaf (circumambulation) around the House of Allah, walking between Safa and Marwah, and throwing the pebbles at the Jamarahs are instituted for the remembrance of Allah.” (Reported by Abu Daw’ud and Tirrnizhi who considers it a sound hadith)