It is reported on the authority of Salman Ibn `Amir, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, said: “For the boy there should be an `Aqeeqah. Slaughter (an animal) for him and remove the harmful thing [i.e. the foreskin] from him.” (At-Tirmidhi, an-Nasa’i, Abu Dawood, Ibn Majah)
late Sheikh Ahmad Ash-Sharabasy, professor at Al-Azhar University, may Allah bless his soul, states the following: According to the Sunnah of the Prophet, peace and blessings be upon him, on receiving a new baby, a person should slaughter a sheep on the seventh day of the birth as a sign of celebrating the new-born. This practice is called `Aqeeqah. Other practices peculiar to such special day (the seventh day) involve shaving the head of the new-born and, after weighing it, giving out silver equal to it as a charity. Also, the day witnesses the naming of the child and slaughtering a sheep from which we eat and give out to others in form of present and charity. These acts are addressed to Muslims since a Muslim is always required to follow the very guidance and tradition of Islam in all acts. A disbeliever, before embracing Islam, is not required to observe any of these obligations.
Since Islam wipes away all past sins and renders the person as sin-free as the day he was born, a new Muslim is forgiven for all acts of the past. Thus, a new Muslim is not obliged to offer `Aqeeqah for himself or for his baby who was born before his conversion.