There is no legal text from either the Qur’an or the Sunnah that orders women to pierce their ears. Piercing ears for women is a cultural practice that is permissible in Islam according to the tacit approval of the Prophet (peace and blessings be upon him).
Sheikh Muhammad Iqbal Nadvi, director and imam of Al-Falah Islamic Center, Oakville, Ontario, Canada, states the following: It is a cultural practice to pierce ears. However, there is no text in the Islamic sources (mainly the Qur’an and the Sunnah) to go against it. What we know from history is that some female Companions used to wear qurt or earrings, and we have no text to show that Prophet Muhammad (peace and blessings be upon him) forbade it.
So, according to the tacit approval or the taqrir of the Prophet, it is acceptable. The same rule applies to piercing the nose.