Can I apply for citizenship or a green card for someone already in the US?

First hire an immigration attorney and then sponsor your husband. My contact info is available on LawQA.

If you are married to someone with no legal status, you need to have a consultation with a competent immigration attorney to discuss if your spouse is eligible. If he entered illegally, then he is not eligible to obtain a green card in the US unless he fits into a law called 245i. That is where an employer or family member filed specific paperwork for him or sometimes a family member, before April 30, 2001. Otherwise he needs to leave the US and apply for a green card through the three step consular processing stage. If he has been in the US more than 180 days with no authorization, he will then be subject to a three or ten year reentry bar. You then must file an extreme hardship waiver to try to get that waived early. This is an intense process so I really recommend you make an appointment. Additionally you want to see if he has other eligibility such as asylum or a U visa!