The obligation of Sefirat Ha'omer falls under the category of "Misvot Ase She'ha'zman Gerama" – Misvot that apply only in a certain time-frame. Halacha generally exempts women from the Misvot in this category, and, as such, women are exempt from the obligation of Sefirat Ha'omer. The question thus arises as to whether women may nevertheless count the Omer if they so desire, and, if so, whether they may recite the Beracha over the counting.
Regarding the second question, it is clear that Sephardic women should not recite a Beracha over the counting of the Omer. Sephardic practice follows the ruling of the Shulhan Aruch that a woman who chooses to perform a Misva from which she is exempt cannot recite the Beracha. Since she is not included under the obligation, she cannot recite the text, "Asher Kideshanu Be'misvotav Ve'sivanu" ("…Who has sanctified us with His commandments and commanded us…"). Thus, for example, a woman who wishes to shake the Lulav on Sukkot may certainly do so, though she may not recite the Beracha of "Al Netilat Lulav," since she is not bound by this Misva.
In the case of Sefirat Ha'omer, however, a number of authorities ruled that a woman should not even count the Omer without a Beracha, because according to Kabbalistic teaching this Misva has no relevance to women. This is the ruling of the Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909), in his work Rav Pe'alim, and of the Kaf Ha'haim (Rabbi Yaakov Haim Sofer, 1870-1939). Hacham Ben Sion Abba Shaul (Israel, 1924-1998) likewise follows this position in his work Or Le'sion (vol. 3).
Summary: Women are exempt from the obligation of Sefirat Ha'omer, and it is preferable for them not to count the Omer.