If you are asking this question in terms of actual practice, then you should direct your question to your local, qualified Rav. The specifics of your situation would determine your practice.
If you are asking is it possible for a woman to be permitted, the short answer is yes. The details of the reasoning behind the decision are found in Igrot Moshe, Volume 3, Even HaEzer, section 1, Siman 57. In keeping with the wishes of the author, Rabbi Moshe Feinstein, not to translate his responsa, you will need to look at the actual letter for details.
It's worth pointing out that this ruling by Rabbi Feinstein is considered very lenient in many circles. Details can be found in English in Halichos Bas Yisrael, volume 1, chapter 5, halacha 5 on page 86, note 9.
Another point worth noting is that according to many, the concept of a woman covering her hair is likely not restricted to married women. It may also apply to unmarried women who have had sexual relations outside of marriage. This is discussed in the responsa of Tzitz Eliezer, volume 15, Siman 55.