ATF Wrongful Reclassification Act This bill amends the federal criminal code to modify the definition of "armor piercing ammunition." Currently, armor piercing ammunition includes certain projectiles or projectile cores that may be used in a handgun. The bill limits that definition of armor piercing ammunition to certain projectiles or projectile cores that are designed and intended by the manufacturer solely for use in a handgun. The bill also revises the standard for determining when armor piercing ammunition is exempt from federal prohibitions on import, manufacture, and distribution. Current law exempts armor piercing ammunition that is primarily intended to be used for sporting purposes, as determined by the Bureau of Alcohol, Tobacco, Firearms and Explosives. This bill replaces the "sporting purposes" standard with a new standard that exempts armor piercing ammunition that is primarily intended by the manufacturer to be used for lawful purposes.