SAN FRANCISCO—After victories in Oregon; Washington, D.C.; and Alaska, marijuana-legalization supporters are setting their sights on the next battleground: California.

The state is expected to play an anchor role in a push for pot legalization in the 2016 election, said Ethan Nadelmann, executive director of the Drug Policy Alliance, which backed this fall’s legalization campaigns. He said measures would likely be on the ballots in Maine and Nevada and somewhat likely in Massachusetts and Arizona then.

...