There is nothing wrong in reciting the Qur’an while performing Tawaf around the Ka`bah.

In this regard, we will cite what Sheikh Sayyed Sabiq states in his well-known book, Fiqh As-Sunnah:

“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 means of remembering Him. `A’ishah reported that the Prophet (peace and blessings 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 Dawud and At-Tirmidhi)”