You clarified that you have an H4 visa. As you know, you are not normally permitted to work under an H4 visa. Even unpaid tutoring might be considered a violation of the H4 terms. So you would need to first change your visa status by either:
- Applying for a green card
- Getting your own H1B or other work visa
As far as getting your own H1, unless you are located in a place where there is an absolute dearth of available faculty, I think it highly unlikely that a community college will sponsor a work visa for you. The amount of paperwork that needs to be done is tremendous (the Department of Labor certification itself is an inch thick)-- as well as the filing costs and attorney's fees. They may also have no experience doing this, unlike the international scholar's office at a larger institution. Finally, many CC faculty are part-time so you may not even qualify for a H1B to begin with.
I would ask your spouse to apply for permanent residency for the both of you and then go on the job market once you have employment authorization.