The new chairman of the Senate Finance Committee said yesterday that Congress should begin work immediately on a tax cut and not wait to cut the budget before it acts.

Sen. Robert Dole (R-Kans.) urged the Reagan administration to devote itself to economic policy "constantly" for its first few months in office and to move swiftly to develop a tax policy. Some congressional Republicans have been impatient with the pace of work on the new economic policy.

Dole said he hoped to know more about this after a breakfast meeting tomorrow morning between some senators, and members of the Reagan team, including David Stockman, director-designate of the Office of Management and Budget, and Martin Andrson, chief domestic policy adviser. This will be the second such meeting this week hosted by Sen. Howard Baker (R-Tenn.).

"I don't believe we can wait until we make all the budget cuts and put those cuts in place, before we have tax reduction," Dole told a luncheon meeting at The Washington Post. A "noninflationary, supply-side" tax cut was "our first big responsibility in this new Congress," he said.

There is apparently disagreement in the Reagan team about whether tax cuts should be balanced against spending cuts next year.

Dole predicted a tax cut of between ,$30 billion and $39 billion this year, which would include accelerated depreciation for business, a cut to 20 percent in the maximum capital gains tax rate and some reduction in personal taxes to go toward offsetting the increase in Social Security taxes from the beginning of the year. He said he would like to get rid of double taxation on dividends, too.

He noted that Reagan's choice for Treasury secretary, Donald T. Regan, whom Dole described as an "outstanding choice," this week reiterated the president-elect's commitment to the controversial Kemp-Roth plan for a 10 percent cut in tax rates for three successive years. Dole said it would be his job to push, or pull, Reagan's economic policy through Congress. But he admitted that he doubts that Kemp-Roth would pass "undiluted" through Congress.

He made a plea for administration cooperation with tax writers on the Hill, saying he would like "to be there on the take-off as well as the landing" and did not want to have a bill "landed in his lap" without being consulted about its contents. However, he said he had been assured on this point.

The Social Security system was another major area which his committee should tackle, the senator said. This will run out of money by February of next year if no measures are taken, Dole added. He said there are no "painless" options: Either the payroll taxes have to be raised, benefits reduced, money transferred from general revenues into the Social Security trust fund, or "we have somehow to figure out a way of restraining the growth in the Social Security program." He said they would be attempting the latter.

On spending, the senator said there is strong bipartisan support on the Finance Committee for "reasonable restraint." Entitlement programs would have to be looked at, he added, but said the Republicans should avoid loading the burden of cuts onto social programs.

Dole strongly criticized House Speaker Thomas P. (Tip) O'Neill (D-Mass.) for keeping the Ways and Means Committee weighted heavily with Democrats. Tax legislation should go through the House first, under the Constitution, but O'Neill's decision could encourage the Senate Finance Committee to take the initiative on tax-writing, its new chairman said.

Ranking Ways and Means Republican, Barber Conable of New York said this week he feared the House may lose the intitiative on tax-writing if House Democrats are obstructive of Reagan's proposals.