wa 'alaykum salam wa rahmatullah
There are slight differences of opinions on this matter, but what is generally taken as the strongest opinion by the scholars, is that it is permissible.
Here are some ahadeeth from the time of the Prophet 'alayhi salaatu wa salaam indicating that ear piercings were done and accepted during that time:
1 – It was narrated that Ibn ‘Abbaas (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) came out and prayed, then he delivered a khutbah – and he did not mention any adhaan or iqaamah – then he went to the women and exhorted and reminded them, and told them to give charity,
and I saw them taking off their earrings and necklaces and giving them to Bilaal, then he and Bilaal went back to his house.
Narrated by al-Bukhaari (4951) and Muslim (884).
According to another report narrated by them both:
They started throwing their earrings and necklaces.
2 – It was narrated that ‘Aa’ishah (may Allaah be pleased with her) said: Eleven women sat and promised one another that they would not conceal anything about their husbands … the eleventh one said:
My husband is Abu Zar’ and what (can I say about) Abu Zar’? He has given me many ornaments and my ears are heavily loaded with them. … ‘Aa’ishah said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: I am to you as Abu Zar’ was to Umm Zar’.
Narrated by al-Bukhaari (4893) and Muslim (2448).
You can find the full fatwa in regard to this at this link:
Women Ear Piercings
Allaah knows best
wasalam