Yes, Muslim women are allowed to wear nail polish. There is no explicit prohibition against it in the Quran, and therefore many scholars believe that it is permissible. However, there is some debate on the matter, as some interpret a hadith which says that the best of women are those who are like men to mean that women should not adorn themselves with things like nail polish which make them stand out from men.
In the end, it is up to each individual woman to decide whether or not she wants to wear nail polish. If she feels that it is something that would help her fulfill her religious obligations and make her feel more connected to Allah, then there is no reason why she shouldn't do so. However, if she feels that it would be a hindrance to her worship or make her stand out in an unwelcome way, then she may choose not to wear it.