Can Islamic women wear Neil polish?

Mostly they are allowed to,

yet, you need to know that in Islam there are many sects such as Sunni and Shii, whithin each you will find several doctrines and fatwas on such issues (i.e, in Sunni sect you may find Hanbali and Shafei).

In main stream Sunni sect women are allowed to wear nail polish, only they have to remove it for Woudou: the ritual of washing certain parts of the body in preparation for prayers. In Shiite, most commonly It's allowed even during Woudou.

Some very minor doctrines prohibit it totally.