Crop Insurance Accountability Act of 2013 - Amends the Food Security Act of 1985 to make a producer violating certain conservation requirements under the highly erodible land or wetland programs ineligible for insurance premiums paid by the Federal Crop Insurance Corporation (FCIC).

Gives producers under the highly erodible land program who are: (1) affected by this change for the first time five reinsurance years to develop and comply with an approved conservation plan, and (2) in violation two reinsurance years to develop and comply with an approved conservation plan.

Gives producers under the wetland conservation program who are: (1) affected by this change for the first time two reinsurance years to remedy a violation, and (2) in violation one reinsurance year to initiate an approved conservation plan.

Requires producers to file a conservation plan with the Department of Agriculture (USDA) in order to receive federal subsidies for their crop insurance premiums.

Provides for: (1) all appeal processes to be exhausted before producers are found to be out of compliance, and (2) a one-year good faith compliance extension.