Dancing with the Torah
Dancing with the Sefer Torah has been the practice for centuries. This applies to men and also to women.
As worded by Maimonides, the rule is, “Anyone who is ritually impure, even a niddah (a menstruant)… is permitted to hold the Torah scroll and dance with it” (Hilchot Sefer Torah 10:8). Rashi notes that there are women who refrain from entering the synagogue when they are niddot (Sefer HaOrah 2:1).
It is not customary for women to follow public practices including dancing when the congregation is assembled, but these days there are increasing numbers of women who enjoy their own hakafot (Torah circuits) on Simchat Torah.