You can petition for your spouse but it will take several years. She will have to find her own visa. If she is married to an LPR it will be less likely that she will be granted a student visa. You may want to wait untill you are a U.S. Citizen to marry her.
Legal disclaimer: This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Do not rely on this advice without speaking to an immigration attorney in detail about your case. This message does not create an attorney-client relationship.
If she comes on a student visa and gets married afterwards, there could be a problem when trying to adjust status because you must have intent to return to your home country when you get a student visa. If you get married as an LPR it will take several years for a visa to be available to your spouse. The fastest and least risky way (depending how long you've been an LPR) may be to naturalize first and then petition. Call me for a consultation.
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She probably would not be issued an F-1 visa once you are married.
You should retain an experienced immigration lawyer to review all the facts and advise you accordingly.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.