NEWARK—Senator-elect Cory Booker sees revamping drug policies as one of the principal issues he can champion once he takes office in Washington, D.C., and he believes he can draw bipartisan support on the issue—even among those who supported his Republican challenger in the special-election race.

Mr. Booker said he has had initial conversations with Senate Majority Leader Harry Reid about his opinions on the issue—such as eliminating mandatory minimum-sentencing laws for nonviolent offenders and reducing incarceration rates...