I am a US citizen, my girlfriend is an illegal alien. Can I adjust her status through marriage?

Maybe, you will need to find a joint sponsor. As to your girlfriend: it all depends how she entered the country. If with visa, she should be ok, depending on a visa, of course. Or, she might need a waiver. I suggest you meet with an attorney to discuss her situation.

It depends on how your girlfriend entered the country. If she entered with a tourist visa and stayed, for instance, you could adjust her status for her to get a greencard, provided you make enough income or you find a joint sponsor. If she entered illegally, the process is longer and more complex - and might require a provisional waiver which will be available in March. I highly recommend you meet with an attorney to discuss your options.

Your girlfriend must have entered the US lawfully for her to adjust status. Otherwise she must leave the US and apply through a US Consulate and may require a waiver for unlawful presence. You should consult with an immigration attorney regarding her options.