All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If this girl is Muslim and there is no (Sharee‘ah) impediment to marrying her, such as her committing acts of Bid‘ah (religious innovations) that take the doer out of the fold of Islam or being unchaste, then it is permissible to marry her. However, the Islamic Sharee‘ah urged Muslims to choose a religiously committed wife. It was narrated on the authority of Abu Hurayrah that the Prophet, sallallaahu ‘alayhi wa sallam, said: “A woman is married for four (reasons): her wealth, her family lineage, her beauty, and her religion (religious commitment). So choose the religious one, lest you be a loser.”
Ibn Qudaamah said in Al-Mughni: “It is recommended for the one seeking a wife to choose a religiously committed one…” [End of quote]
Marriage is a long journey that requires a significant level of compatibility between the spouses for their married life to last. Moreover, a woman is entrusted with her husband’s wealth, her own self, and his children; she is responsible for raising them, and many qualities are passed on from her to them. Therefore, carefulness and patience should be observed while choosing a wife, and one should strive to find a righteous woman. It was narrated on the authority of ‘Abdullaah ibn ‘Amr that the Messenger of Allah, sallallaahu ‘alayhi wa sallam, said: “The worldly life is (a quick passing) enjoyment; and the best enjoyment of the worldly life is a righteous woman.” [Muslim]
If you marry her when she is in such a state, you are Islamically required to enjoin her to do good, forbid her from evils, oblige her to wear the Hijaab, and prevent her from Tabarruj (unlawful exposure of beauty). She is a trust with you, and you shall be held accountable about her before Allah, The Exalted, on the Day of Resurrection. Allah Says (what means): {Men are in charge of women…} [Quran 4:34] Tafseer As-Sa‘di reads: “It means that men are guardians over them (their womenfolk) by enjoining them to fulfill the rights of Allah, such as observing His obligations and preventing them from committing evil acts, and men must oblige them to do that…” [End of quote]
If she obeys you, then it is good, but if she refuses, you have two options that are both bitter: you keep her as wife despite her state, which may negatively affect your religiosity and faith, or you divorce her. You should decisively refrain from marrying a woman who is not steadfast upon obeying her Lord. You are bound to find a righteous woman, Allah willing, so strive in seeking a righteous wife with the help of Allah, The Exalted, and then your Muslim brothers whom you trust.
Allah Knows best.