In a sudden move toward consolidating Republican control of the nation's public broadcasting, President Reagan has named New York industrialist William Lee Hanley Jr. to replace Democrat Gillian M. Sorensen on the board of the Corporation for Public Broadcasting.

The appointment Monday brings the balance on the board to seven Republicans and seven Democrats. It came on the eve of today's annual board meeting, in which CPB policy will be set for the coming year and in which Sharon Percy Rockefeller, a Democrat, will seek a third one-year term as board chairman.

The White House will soon announce another appointment to fill a vacancy on the 15-member board, according to a congressional source.

Assuming the next appointment is Republican, this would give Republicans undisputed control--eight members, with seven appointed by Reagan and one by Gerald Ford--of the organization that passes federal funds to National Public Radio and its television counterpart, the Public Broadcasting Service.

Rockefeller escaped virtually unscathed last spring from the financial crisis at the radio system in which NPR officials ran up a $9 million debt and avoided bankruptcy only because of a loan of federal funds from CPB. CPB officials said they had general oversight responsibilities for NPR but were not responsible for the debacle.

Because CPB holds the purse strings, a change in the political coloration of its board may strongly affect NPR's future. The General Accounting Office has been ordered to investigate what happened at NPR, and hearings in both the House and Senate are planned for this month or next.

Rockefeller's CPB chairmanship may be threatened by the change on the board. The current vice chairman is Republican Sonia Landau, a corporate consultant appointed by Reagan in 1981. She unexpectedly unseated Democratic civil rights attorney Jose A. Rivera as vice chairman last year.

The chairman, vice chairman, president and other corporate officers are chosen by majority vote of the board, which by law may have no more than eight members of the same political party.

Hanley was named Monday in an unusual recess appointment. Made with Congress out of session, recess appointments do not require the usual Senate confirmation. Nevertheless, the CPB board met in executive session yesterday, and a CPB source said the board was likely to discuss whether to challenge the appointment.

If the appointment is challenged it will cast a cloud of legal uncertainty over any CPB board action taken today, a CPB source said. Sorenson's appointment by former President Carter expired in March 1982, but by law she retains her seat until a replacement is appointed. This did not happen until Monday.

An aide on Sen. Barry Goldwater's (R-Ariz.) communications subcommittee, which must approve normal CPB board appointments, said the White House had fully informed Goldwater about the Hanley appointment. The aide said Goldwater had no objection to the appointment.

The aide said the subcommittee was told by the White House there should be another CPB board appointment "fairly soon."

Hanley, 43, is chairman of Hanley Inc., a brick manufacturing and oil exploration corporation. He was Connecticut coordinator for the Reagan-Bush campaign. His secretary said he left his office in New York for Washington at noon yesterday, but a source said he did not appear at the closed-door CPB board meeting. Hanley could not be reached for comment.