Paul C. Warnke, formerly chief negotiator for the SALT II talks, Edward A. McCabe, chairman of the Student Loan Marketing Association, and James D. Cope, president of The Proprietary Association, have been named directors of the First American Bank of Washington.

First American Bank of Washington is one of six banks owned by First American Bankshares Inc., a multistate bank holding company based in Washington. First American Bankshares, which also holds banks in Virginia, Maryland, New York and Tennessee, is controlled by a group of Middle Eastern investors.

Warnke, who returned to private law practice in 1978, currently is a partner with the chairman of First American Bankshares Inc., Clark M. Clifford, in the Washington firm of Clifford & Warnke.

A highly visible figure under the Carter administration, Warnke, 65, was director of the Arms Control and Disarmament Agency and chief negotiator for the SALT II talks from 1977 to 1978. He also has served as an assistant secretary of Defense for international security affairs, and as a special consultant to the secretary of State.

Edward A. McCabe, a retired Washington attorney, has been chairman of the board of the Student Loan Marketing Association, the nation's largest source of financing for insured student loans, since its founding in 1973.

McCabe, 68, was counsel and administrative assistant for the Eisenhower administration from 1956 to 1960 and has since served as a transition consultant to the White House. He attended the University of Maryland and Columbus University in Washington, and completed his legal education at the Columbus University School of Law, now the Catholic University Law School.

James D. Cope, 53, is president of The Proprietary Association, a trade association representing manufacturers of over-the-counter medicines. He also serves as vice chairman of the World Federation of Proprietary Medicine Manufacturers and on the boards of the Council of Family Health and the Ophthalmic Research Foundation.

The three new board members are replacing George E. Hamilton Jr., a partner with Hamilton & Hamilton, who is retiring after 54 years with the bank; Henry E. Catto, vice chairman of H & C Communications Corp., and Frank N. Ikard, a partner in a Washington law firm.