Answer

In the Name of Allah, Most Gracious, Most Merciful. 

All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.

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In this fatwa:

In responding to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:

 During Tawaf, one is free to engage in dhikr and duaa. Reading the Quran is the perfect form of dhikr. Therefore, one may read it from memory after making the essential duaas associated with tawaf.

However, one should avoid reading from the Mushaf in large crowds. By doing so, one may inconvenience others. It may also amount to dishonoring the Quran.

Almighty Allah knows best.