I want to know the rule for the one who marries an American woman to get legal status.

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 American lady is Jew or Christian and if she is chaste, it is lawful to marry her. Allah Says (what means): {(Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time.} [Quran 5:5]

It is a condition that this marriage be carried out according to the rulings of the Sharee’ah. It should not then be limited to a given period agreed upon by the two sides. However, one should know that marrying women from the People of the Book can have bad consequences particularly on the children if there happen to be any. There are many heartening stories in this subject. The above-cited ruling is about normal marriages.

As for the kind of marriage you mentioned (marriage to get legal status in America or for other specific purposes), then this kind of marriages fits into one of three following categories.

First, if the man marries this woman with the intention of having a wife and the intention of residence or nationality, this marriage is valid and having the intention of getting the nationality does not influence the validity of this marriage as a woman can be married for her wealth or lineage as narrated in the sound Hadeeth.

Second, if the intention of this man is only to get legal status in this country and he is intending to divorce her as soon as he gets that status and she does not know about this, then this marriage is also valid and it is not considered as a temporary marriage as there is no agreement between them beforehand on a specific period after which they get divorced.

But this kind of marriage can have consequences that would make it closer to being unlawful than to being lawful. It can cause harm to the woman whose rights should be looked after and also it can be a source of defamation to the religion itself.
It could be considered as cheating the woman who might not have accepted this marriage in the first place had she known the intention of the man (i.e., to divorce her as soon as he legalizes his status). Abu Hurayrah narrated that the Prophet said: “Whoever cheats us is not one of us.” [Muslim]

Third, if the intention of the man is only to get legal status and the woman knows it and there is a common agreement that he will divorce her and give her a certain amount of money after a specified period sufficient to get him the green card he needs, this marriage is unlawful according to the Sharee’ah as it fits under the category of temporary marriage.

On the other hand, we would like to remind the questioner of the rulings concerning living in or traveling to non-Muslim countries which are explained in Fataawa 81642, 86405, 377986, 369667, 89879, 88291 and 81464, 81142 and 81464.

Allah knows best.