The Congregation Orah Saddiqim website aptly states:

ROLES OF WOMEN
In Karaite law, female witnesses are just as good as male witnesses. Karaites have never made a distinction between the two - both witnesses are valid in any legal situation.

Women have always been able to hold leadership roles. This was true even in the Middle Ages, the height of misogyny. In the 11th century, in Spain, after the Rabbanites killed the Karaite leader Sidi ibn al-Taras, his wife, al-Mu‘alima (which means the teacher), took over for him as the leading Hakham of the Karaites in Spain.

From Tehillim [Psalms]we know that women used to sing in the Beit Hamiqdash [Temple]. Tehillim [Psalms] 46:1, 68:26 are Psalms that were written specifically for women to sing, and accompany with dancing and the playing of instruments. Consequently, women in Karaite Judaism have never been constrained from singing or speaking in the Beit Kenesset [synagogue]. As one might conclude from this, women can, in fact, hold the position of Hazzan [one who leads the prayers]. Again, no religious role in Karaism is forbidden to women.