Secretary of State-designate George P. Shultz has picked a career Foreign Service officer as his executive assistant at the State Department, but a widely rumored candidate to be Shultz' top deputy has taken himself out of consideration for the job.

The Foreign Service officer, Raymond G.H. Seitz, is the first official selected by Shultz since he was named to succeed Alexander M. Haig Jr.

Seitz, 42, has served in Canada, Africa and London as well as several posts in the State Deparment in Washington, including the executive secretariat. His most recent job was that of deputy assistant secretary in the Bureau of Public Affairs.

Meanwhile, the person most widely rumored to be Shultz' likely choice as deputy secretary of state, Lawrence H. Silberman, has made it known he would not take the job for what friends called personal reasons.

Silberman, executive vice president of Crocker National Bank in San Francisco, was solicitor of the Department of Labor in 1969-70 when Shultz was secretary of labor. Later Silberman served as undersecretary of labor, deputy attorney general and ambassador to Yugoslavia.

In the past several years both men have been business executives in the San Francisco area, where Shultz was president of Bechtel Group Inc.

Silberman is considered both strongly conservative and pro-Israel and thus, in the view of some, a logical counterpoint to Shultz' centrist tendencies.

Last Wednesday Silberman was recommended for the deputy secretary's position by a group of conservative leaders who called on presidential counselor Edwin Meese III to ask for consideration in new State Department appointments, according to a participant in the meeting who asked not to be identified.