Fiqh-us-Sunnah Volume 5, Hajj and ‘Umrah, Fiqh 5.080.
Section : Making a Tawaf while Riding.
A person may, even if he is able to walk, perform tawaf while riding, provided there is a valid reason for doing so.
Ibn ‘Abbas reported that during the Farewell Pilgrimage the Prophet (peace be upon him) performed tawaf while riding his camel, and touched the Black Stone with a stick (that he carried). (Reported by Bukhari and Muslim)
Jabir reported that during the Farewell Pilgrimage the Prophet (peace be upon him) performed tawaf and made Sa’i between Safa and Marwah while riding on his mount, so as to show it to the people, to draw their attention, and (to give them an opportunity) to ask him any questions (they had), and the people were crowding around him.”