There is no hadith of the Prophet or a practice of the companions to support making tawaf and dedicating its reward for a dead or for a living Muslim.

There are numerous hadiths which confirm the act of dedicating complete `Umrah, Hajj, running charity and fasting to dead people.

It is recommended that you make tawaf for yourself but you increase making du`aa’ for your deceased relative. Your supplications will benefit him according to the Prophet’s hadith, “When a man dies, his deeds come to an end except for three things: Sadaqah Jariyah (ceaseless charity); a knowledge which is beneficial, or a virtuous descendant who prays for him (for the deceased).” (Muslim).

According to the report of `A’ishah, “The Prophet (peace be upon him) told me to go to Al-Baqi` cemetery and pray for forgiveness for them.” She said,” What should I say, O Messenger of Allah?” He said: “Say: Peace be upon the inhabitants of this place among the believers and Muslims. May Allah have mercy upon those who have gone on ahead of us and those who come later on, and we will join you, if Allah wills.” (An-Nasa’i) It is graded as an authentic hadith.

Almighty Allah knows best.