A person may perform Tawaf while riding, provided there is a valid reason for doing so. Sheikh Sayyed Sabiq states in his well-known book Fiqh As-Sunnah: Even if he is able to walk, a person may perform Tawaf while riding, provided there is a valid reason for doing so.
Ibn `Abbas reported that during the Farewell Pilgrimage the Prophet (peace and blessings be upon him) performed Tawaf while riding his camel, and touched the Black Stone with a stick, which he was carrying. (Al-Bukhari and Muslim)
Jabir reported that during the Farewell Pilgrimage, the Prophet (peace and blessings be upon him) performed Tawaf and made Sa`i between As-Safa and Al-Marwah while riding his mount, so as to draw the people’s attention, and (give them the opportunity) to ask him any questions (they had), and the people were crowding around him.
Allah Almighty knows best.