Yes, if you marry a U.S. citizen, you can usually apply for a green card inside the U.S., even if your F-1 visa is expired

After marriage, you can file Form I-130 (petition) and Form I-485 (green card application)together in a process called adjustment of status.

While your application is pending, you can also apply for work authorization (EAD) and Advance Parole to travel.