Based on the famous rule that women are exempt from all time-bound mitzvot, women are exempt from the mitzvah of counting the Omer, for it is dependant on time (see Peninei Halachah, Tefillat Nashim, chap. 3, for the logic behind this rule).
However, a woman who so desires may perform time-bound mitzvot, and she receives credit for doing so. We thus find that women are accustomed to hearing the shofar on Rosh HaShanah and taking a lulav and sitting in a sukkah [on Sukkot]. But the poskim debate the issue of the blessing. According to the author of Shulchan Aruch (O.C. 589:6), women do not make blessings over such mitzvot, and this is the prevalent custom among most Sefardic women.
The Ashkenazi custom follows the Rama’s opinion, that women who perform time-bound mitzvot are permitted to recite the blessing (see Tefillat Nashim 2:8). However, some Ashkenazi poskim rule that women should not recite a blessing over the Omer count because they do not pray [Ma’ariv] in the synagogue and are therefore more likely to miss a day. As we learned above, one who forgets to count a day is not allowed to continue counting with a blessing, and perhaps a particular woman will not realize that she forgot to count and will continue counting with a blessing (M.B. 489:3). Others say that women shouldn’t count the Omer for kabbalistic reasons (Rav Poalim, part 1, end of 10, 12). On the other hand, still others claim that the Askenazi custom is for women to count (M.A. 489:1).
Therefore, a woman who knows that she can make it through the entire count, and even if she misses a day, she knows to continue counting without a blessing, may count with a blessing, according to Ashkenazi practice. This is especially true regarding a woman who prays Ma’ariv every evening or whose family members are in the habit of reminding her to count. She may count with a blessing, if she is Ashkenazi and so desires, because the chances of her forgetting to count are relatively small.
