Somerset's mayor and Town Council have rescheduled a referendum on a resolution backing a nuclear-weapons freeze by the United States and the Soviet Union.

The council has taken no stand on the measure, but would consider the referendum results as advice from residents on whether the town should join the growing number of localities seeking an end to the nuclear arms race.

Voting on the question, originally scheduled for June 1, has been moved to 8 p.m. June 21 at Somerset Elementary School, 5811 Warwick St. The election also will decide who will fill the council vacancy left by A. Eugene Miller, who was elected mayor May 3. Residents also will vote on the town's property tax rate and new budget.

The council set for 8 p.m. June 14 a public forum featuring Jeremy Stone, head of the American Federation of Scientists, who will speak in favor of a weapons freeze, and Ronald Lehman, U.S. deputy assistant secretary of Defense for Strategic and Theater Nuclear Forces Policies, who will present the Reagan administration's stand on nuclear arms.

The speeches, to be followed by audience discussion of the issue, also will take place at Somerset Elementary School.