Sayyiduna Abdullah bin Abbas (may Allah be pleased with him) said: I gave the Prophet (peace and blessings be upon him) Zamzam water to drink and he drank it standing; he (peace and blessings be upon him) was at the House when he (peace and blessings be upon him) asked for water.
In none of their narrations is the tawaf mentioned, and Allah knows best.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9299