Yes, a green card holder (LPR) can petition for a spouse using Form I-130, and once a visa is available, you may be able to adjust status.

 If you are in the U.S. legally (e.g., on a valid visa and haven't overstayed), you may be able to adjust status without leaving the country once your priority date is current.

 If your spouse becomes a U.S. citizen during the process, your case may speed up you could adjust status immediately if you're in the U.S., even if you overstayed.