Haiti and Armenia Reforestation Act of 2013 - Authorizes the President to: (1) provide Haiti and Armenia with financial assistance, technology transfers, or capacity building assistance to reduce deforestation and increase afforestation and reforestation; (2) establish a grant program to reverse deforestation and improve reforestation and afforestation in Haiti and Armenia; (3) make grants to nongovernmental organizations for the open-market purchase of discounted government of Haiti debt in exchange for forest restoration commitments by the government; and (4) forgive debt owed to the United States by the government of Armenia in exchange for forest restoration commitments by the government.