Is it possible for congress to delegate voting on specific policies to a nationwide popular vote at the federal level? If so, how would this be accomplished?
There is not currently a way for the federal government to hold a national vote on anything, including referenda. All elections in this country officially happen at a state level (or lower).
Remember, in presidential elections, voters in each state pick electors who compromise the Electoral College. (In a certain sense, the Electoral College itself conducts a national vote, but since there are only 538 electors, it's not really the same.)
The National Initiative movement supports the creation of a system that would allow the kind of federal referendum. In order to do this, the US Constitution would need to be amended to explicitly give US citizens the right to vote on policies.