Preventing Victims of Stalking Act of 2013 - Amends the Brady Handgun Violence Prevention Act to prohibit the sale or other disposition of a firearm or ammunition to any person knowing or having reasonable cause to believe that such person: (1) is subject to a court order that restrains the person from harassing, stalking, or threatening any individual (currently, an intimate partner of such person or child of such partner or person), or engaging in other conduct that would place any individual in reasonable fear of bodily injury; or (2) has been convicted in any court of stalking. Prohibits any such person from shipping or transporting any firearm or ammunition in interstate commerce, possessing any firearm or ammunition in or affecting commerce, or receiving any firearm or ammunition which has been shipped or transported in interstate or foreign commerce.