BankAmerica Corp., the San Francisco company that owns the nation's biggest bank, said late today it plans to acquire Charles Schwab & Co., the country's second biggest discount stock brokerage firm.

If the merger is approved by the government, it apparently will be the first time since the Depression that a bank-related company has moved into the securities brokerage business.

Banks long have complained that brokerage firms and insurance companies have been encroaching on areas that traditionally have been in the domain of banks--such as taking deposits--while commercial banks have been prevented from expanding some of their activities.

Schwab, as a discount broker, primarily buys and sells stocks and bonds for customers at low fees, but does not provide other services offered by full-service brokerage firms such as investment banking, research and commodities.

Schwab and BankAmerica signed a letter of intent under which the giant bank holding company would exchange 2.2 million shares of its stock, worth about $53 million, for the brokerage firm.

The acquisition, however, will need approval of the Federal Reserve Board. The central bank rules on what activities are permissible for bank holding companies, corporations like BankAmerica that own commercial banks. A spokesman for the Federal Reserve said that owning a brokerage firm is not now on the list of approved activities for bank holding companies.

The Fed could rule on the acquisition on an ad hoc basis or it could start a rulemaking procedure to determine whether owning a brokerage firm is a permissible activity for all bank holding companies.

The face of the financial industry has been changing rapidly in recent months as companies have sought to increase the number of financial services they can offer customers. Prudential, the largest insurance company, bought the Bache Group Inc., the second-biggest brokerage firm. Giant American Express purchased the second-biggest broker, Shearson Loeb Rhoades Inc. Sears, Roebuck & Co., the nation's biggest retailer, just purchased the country's biggest real estate services firm, Coldwell Banker, and the fifth-biggest securities firm, Dean Witter Reynolds Inc. There have many other mergers among financial services companies this year.

Samuel H. Armacost, president of BankAmerica Corp., which owns the Bank of America, said the acquisition of Schwab will enable BankAmerica to "provide a broader range of services," especially to consumers.

Schwab, which has offices in the Washington area, had revenues of $42 million in the year ended Sept. 30.