Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Muslim women can call the adhan amongst women. In the general mosques, the sunnah is that males give the adhan not women.
Answering your question about if women can call the adhan, Dr. Jasser Auda, Professor and Al-Shatibi Chair of Maqasid Studies at the International Peace College South Africa, states:
Yes, Muslim women can call the adhan amongst women. This is what Aishah (may Allah be pleased with her) used to do. She used to call the adhan and the iqamah and lead other women in prayer.
However, there is no evidence that women can call the adhan for men and women except in a family setting, where women can call the adhan and even lead the prayer.
Umm Waraqah, daughter of Abdullah ibn al-Harith (may Allah be pleased with her) used to lead her family in the family setting including males. Prophet Muhammad (peace be upon him) used to visit her at her house. He appointed a muezzin to call adhan for her; and he commanded her to lead the members of her house in prayer. (Abu Dawud)
In the general mosques, the sunnah is that males give the adhan not women.
Almighty Allah knows best.