The measure is being unveiled on Capitol Hill Tuesday by Paul and Democrats Kirsten Gillibrand of New York and Cory Booker of New Jersey.
The bill could help the libertarian-leaning Kentucky Republican stand out in what is shaping up to be a crowded field ahead of the 2016 presidential election.
It will aim to eliminate the uncertainty surrounding use of marijuana in the states that allow it for medicinal purposes. Medical marijuana is now legal in 23 states and the District of Columbia, and voters have approved it for recreational use in four states and Washington, D.C.
Advocates say that even in those states, the federal prohibition on marijuana prevents doctors at veterans’ facilities from prescribing it for medical purposes and makes access difficult.
Marijuana legislation has been introduced in the House. Advocates say the introduction of a high-profile Senate bill is a sign of growing acceptance.
Some 46 percent of Americans support full legalization of marijuana, according to Reuters/Ipsos polling. Some 58 percent of Republicans oppose legalization, while 58 percent of Democrats support it.
Former Florida Governor Jeb Bush, Texas Senator Ted Cruz, Florida Senator Marco Rubio and Texas Governor Rick Perry have said that states should have the right to determine their own marijuana laws.
But one marijuana advocate said the potential Republican candidates have been “all talk” so far.
“It’s nice to see that Senator Paul is actually doing something about it,” said Dan Riffle of the Marijuana Policy Project, a pro-legalization group.