"The Senate has not yet provided its advice and consent, and may not provide such consent," he wrote.
In addition to questions about the Second Amendment, Corker said many of the treaty's provisions regarding arms sales will require congressional approval.
The treaty will require countries that ratify it to establish national regulations to control the transfer of conventional arms and components and to regulate arms brokers. It will not control the domestic use of weapons in any country.
It prohibits the transfer of conventional weapons if they violate arms embargoes or if they promote acts of genocide, crimes against humanity or war crimes, and if they could be used in attacks on civilians or civilian buildings such as schools and hospitals.
The treaty covers battle tanks, armored combat vehicles, large-caliber artillery systems, combat aircraft, attack helicopters, warships, missiles and missile launchers, and small arms and light weapons.
In considering whether to authorize the export of arms, a country must evaluate whether the weapons would be used to violate international human rights laws or be employed by terrorists or organized crime elements. A country also must determine whether the weapons would contribute to or undermine peace and security.
In addition, the treaty requires countries to take measures to prevent the diversion of conventional weapons to the illicit market.
What impact the treaty will have in curbing the global arms trade — now estimated at between $60 billion and $85 billion annually — remains to be seen. Much will depend on which countries ratify it, and how stringently it is implemented once it comes into force.
U.N. chief Ban Ki-moon and numerous human rights and humanitarian groups hailed the U.S. move, saying it sent a powerful signal to countries that have yet to sign.
"It is of particular significance that the largest arms exporting country in the world, the United States, is now also among those countries who have committed themselves to a global regulation of the arms trade," Ban said in a statement.
Oxfam America called it "a significant victory for human rights and development." Human Rights First urged the Senate to put aside partisan politics to send a "a strong message to those countries committing mass atrocities, like the current Syrian regime, as well as those who are arming them, like Russia."
Frank Januzzi of Amnesty International USA said he hoped the signing would show that the Obama administration "is politically committed to ending the unscrupulous trade in deadly weapons used by dictators, war lords and criminal gangs to commit atrocities."