Women are not obligated in the mitzvah of counting the Omer because it is a positive mitzvah that is dependent upon time. However, many women have accepted upon themselves to count, while others have the minhag for women to refrain from counting. Shulchan Aruch w/Mishnah Brurah 489:1, Minchas Chinuch 306, Avnei Nezer 384
Women may, if they wish, count with a beracha, but their husbands should remind them to count so that they do not miss any days. The minhag of the Steipler was for women within his household to count with a beracha. Orchos Rabbeinu 2:pg92, Piskei Tshuvos 489:7
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