Labeled the "Nutritious SNAP Act," the legislation would do on a national level what a number of states have already done on their own through a waiver process.
Paul argues the food assistance program created to fight hunger is now "fueling a new public health crisis" by continuing to "subsidize soda and junk food."
In a recent interview, the senator said he would like to go further when it comes to restrictions.
"I would probably also say that food stamps should only go to maybe moms with four kids who can't work. That's what they were intended for," Paul said. "But I think an able-bodied 19 (to) 21-year old boy or girl really has no business on food stamps."
Critics of the bans on products labeled "junk food" say creating more hurdles for retailers reduces access for participants and that the SNAP program has shown long-term positive health impacts in its current form.