There is a dispute whether women are required to read/hear parashas Zachor, but the common practice nowadays is that they do so. I wonder whether anyone has argued that they have accepted it upon themselves and are for that reason now required to do so. Any authoritative source to that effect would be valuable, as would any authoritative source that specifically debunks the notion.
I'm sorry this is not a very satisfying answer (least of all to me). But it's too much for a comment, so here goes.
"Latter-day authorities oblige women to listen to Parashat Zakhor, since the Torah does not specify any set time for the mitzvah. Some restrict this obligation to any reference to the story of Amalek; while others require women to listen to Parashat Zakhor at the time set by the Halakhah for public reading."
--Rabbi Getsel Ellison, Serving the Creator: A Guide to the Rabbinic Sources (Women and the Mitzvot vol. 1), 194
On pages 203 through 207, Ellinson details the entire extensive makhloikes about this issue, and comes to the conclusion--perhaps from doubt--that a woman's performance of this mitzvah is in fact required (that is, independent of whether it were the custom of women to perform it).
According to Rav Ellinson in the same book, there is a "difference of opinion among the later authorities as to whether the custom of women performing Positive Precepts dependent upon a set time establishes for them an ongoing obligation, having the force of an unuttered vow to perform a mitzvah. As we pointed out [...], the matter depends upon the dispute between R. Yehuda and R. Yose. Since the Halakhah follows R. Yose, the performance of Positive Precepts dependent on a set time by women is in fact considered as fulfilment of a mitzvah, the customary observance of which transforms it into an obligation" (83-84, note 9) It seems, however--and despite the obfuscatory writing--that this refers only to women's individual "customs" to perform mitzvot (as does, apparently, everything in Ellinson's chapter "Does a Woman's Custom Render the Act Mandatory?," unto everything in the whole book.)
I'm sorry I could not answer your question better and hope you (and I) get a great answer.
According to this article, "The Nitei Gavriel (Purim p. 154) writes that the current minhag for women to go to shul to hear Parshas Zachor, while the Divrei Chaim 2:14 as well as Rav Moshe Feinstein (quoted in Kovietz Halachos, page 13) accept a minhag of women not going to shul to hear Parshas Zachor. Therefore, it seems to be a machlokes of what the custom is for women."
At least for the Sephardi community, Rav Eli Mansour seems to say women have taken upon themselves the stringency of hearing Parshas Zachor, in deference to the view that they are included in the obligation.