Q. Are women allowed to carry a Sefer Torah?

A. Teshuvos Vehanhogos (4: 238: 7) quotes a difference of opinion if women are permitted to stitch and sew the parchments that comprise a Sefer Torah. Although he is stringent, he explains the reason of the
ones who are lenient, namely, that the stitching may not be an essential needed act, also at that stage it is not a Sefer Torah yet. Yalkut Yosef (Tzitzis Tefilin and Safrus p. 679) mentions that there was a tradition in some places to honor women at the siyum ceremony by allowing them to stitch a loop that joins the “yerios” together. However, his opinion is also to be stringent. See also Minchas Aviv (1: p.51) in regards to the mitzva of a woman writing a Sefer Torah.
During the tefilah women pray separately and do not take part in any act that would require them to carry a Sefer Torah.
Shulchan Aruch (Y.D. 282: 9) rules that all people who are in a state of tumah or impurity including women during their period may hold and read a Sefer Torah, as long as their hands are clean. Remoh (O.H. 88: 1) maintains that women even in impurity can touch a Sefer Torah, however the common tradition in their cities was to abstain.
Horav Shlomo Miller’s opinion is that in general women should refrain from carrying a Sefer Torah, if not in need (for the necessary benefit of the Torah). They should therefore abstain from making and dancing their own hakafot carrying a Sefer Torah or taking around themselves a Sefer Torah on the women’s section for the other women to kiss.

 Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a