Yes, you can appeal a marriage-based green card denial, but whether it’s the right option depends on the reasons for the denial. To appeal, you would need to file Form I-290B, Notice of Appeal or Motion, within 30 days of receiving the denial notice. You can either request that USCIS reconsider its decision (a Motion to Reconsider) or that they reopen your case to consider new evidence (a Motion to Reopen).
Alternatively, you can take your appeal to the Administrative Appeals Office (AAO). Keep in mind that appeals can be complex, requiring strong legal arguments and, sometimes, additional evidence to counter the reasons for denial. In some cases, it might be simpler to correct the issues and reapply instead.