Sheikh Sayyed Sabiq states in his well-known book Fiqh As-Sunnah: “It is encouraged to remember Allah and supplicate to Him as much as possible during Tawaf. For this purpose, one may choose any supplication that one feels comfortable with, without restricting oneself to any particular one or repeating what others may be saying. There are no set supplications prescribed for this purpose. The supplications that some people consider to be prescribed for various rounds of Tawaf are not authentic. There are no such supplications reported from the Prophet (peace and blessings be upon him). One should pray for oneself, for one’s family and for the Muslims for anything that is good in this life or the hereafter.
Some of the supplications that are reported in this regard are given below:
1- Upon facing the Black Stone the Prophet (peace and blessings be upon him) said: “Allahumma imanan bika wa tasdiqan bikitabik wa wafa‘an bi`ahadika wa Itba`an li sunnat nabbiyyika bismillahi wallahu akbar. (This is reported directly from the Prophet (peace and blessings be upon him)) (O Allah! I begin this Tawaf believing in You, affirming the truth of Your Book, fulfilling my covenant with You, and following the example of Your Prophet (peace and blessings be upon him). In the Name of Allah! Allah is the Greatest!)”
2- When commencing the Tawaf the Prophet (peace and blessings be upon him) said: “Subhan Allah wal hamdu lillah wa la ilaha illallah wallahu akbar wa la haula wa la quwwata illa billah. (Glory be to Allah! All praise is due to Allah, there is no god but Allah. Allah is the Greatest. There is no might nor power except with Allah).” (Ibn Majah)
3- When reaching the Yemeni corner, the Prophet (peace and blessings be upon him) said: “Rabbana aatina fid dunniyya hasanatan wa fil akhirati hasanatan wa qina ‘azhaban nar (Our Lord! Grant us good in this world and good in the hereafter, and save us from the punishment of the Fire).” (Abu Dawud and Ash-Shafi`i)
4- Ash-Shafi`i said: “Each time I pass the Black Stone I like that one should say ‘Allahu Akbar,’ and while jogging one should supplicate and say: Allahumma ij`alhu hajjan mabruran wa zhanban maghfuran wa Sa`iyan mashkuran (O Allah! Let this be an accepted Hajj, with sins forgiven, and a well appreciated effort).” Also during each round of Tawaf he would say: “Rabbighfir warham wa`fu `ama ta`lam wa antal a`azzul akram allahumma aatina fid dunniyya hasanatan wafil aakhirati hasantan wa qina ‘azhaban nar. (O my Lord! Forgive us, and have mercy upon us, pardon our sins that You only know. You are the Most Honored and Dignified. O Allah! Grant us good in this world and good in the hereafter, and protect us from the torment of the fire).”
It is reported that when Ibn `Abbas was walking between the Yemeni corner and the Black Stone, he used to say: “Allahumma qanni`ni bima razaqtani wa barik lifihi wakhluf `alayya kulla gha’ibatin bikhair. (O Allah! Let me be satisfied with what You have provided me. O Allah! Bless it for me. O Allah! Substitute every good thing that I missed with something good.” (Reported by Sa`id bin Mansur and al-Hakim).”
Allah Almighty knows best.