Health, Education and Welfare Secretary Joseph A. Califano called President Carter yesterday to explain his decision to put a chef - at a cost of $12,763 annually - on the public payroll to prepare his meals.

The President, who has made a point of urging his Cabinet members to forego official frills, said through White House press secretary Jody Powell that "Secretary Califano was concerned . . . and indicated he was going to deal with it."

Powell said Carter had little else to say on the subject. However, an HEW spokesman said Califano's vow (to deal with it" does not means he intends to fire the new chef, Wiley Barnes, who recently retired from the Marine Corpa.

Quite the contrary, said the spokesman, Sanford Winston.

"The secretary said he could justify having him (Barnes) He's not a chef. He's a cook," Winston said.

Winston said Barnes' salary and duties are aki nto those of a shortorder cook. However, he said Barnes is also responsible for planning and preparing meals for large, official HEW functions - such as a recent gathering at the department of 23 members of the National Governors Conference.

Califano described Barnes as a "personal assistant" in the 402-word job description he certified for the Civil Serivce Commission. The official job description never mentioned Barne's as a cook - or a chef.

Winston said Califano needs him because the secretary works a minimum 12-hour day and frequently works weekends at HEW when the department's cafeterias are closed.

Besides that, Winston said: "I don't think we're out of the line at all (in having Barnes), especially when you look at the way the other departments operate."

Winston has a point.

At the Department of Transportation, top executives are fed by four U.S. Coast Guard enlisted men in a 10th floor executive dining room called the Coast Guard Commander's Mess. They pay out-of-pocket for their meals - unless they are eating at an official function.

The "installation" - according to a Transportation spokesman - is operated by Coast Guard for the benefit of the commandant, his staff, and the ranking staff members of the Transportation Department.

Transportation Secretary Brock Adams has eaten in the Commander's Mess once - he usually eats at his desk or grabs a sandwich in the employees' cafeteria, said the spokesman, David A. Jewell.

Jewell said Adams is trying to get a private contractor to operate the executive dining room. "So far, there are no takers from private industry," Jewell said.

At the Department of Justice Miguelino Elias and Jose Valenzuela are paid a total of $32,432 annually to prepare meals for Attorney general Griffin B. Bell, his guests and top assistants.

Elias and Valenzucia have been at their Civil Service jobs at least sever years before bell assumed office in January. They serve daily staff breakfasts, frequent luncheons and meals at special guest occasions.

Justice Department executive breakfasts usually cost $1.50 per person, according to a spokesman. Lunches go for $2.50 Meals at official occasions are paid for out of a department contingency fund, the spokesman said.

And then there is the Treasury Department, where Gladys E. Robinson, hired last December at a salary of $6.24 an hour, holds forth in the executive kitchen. Not a civil service employee, she is distinguished from most of her cullinary colleagues in that she has a "top secret" clearance, which enables her to be present when Treasury Secretary W. Michael Blumenthal is talking government business with official visitors.

A the Defense Department, one parttime military officer, 19 enlisted persons and one parttime civilian oversees the doing in - official title, here - The Secretary of Defense Dining Room. At least 118 top defense executives are entitled to eat in the dining room, at their own expense.

Salaries for the Secretary of Defense Dining Room employees cost taxpayers $173,232 last year.

The Department of Labor has an executive cook, Ted Minor, who is paid $14,900 a year.

The departments of State Commerce, Agriculture, the Interior and Housing and Urban Development, have no executive chefs, according to their spokesmen. In these agencies official function are often catered by outside agencies and regular eating is usually done at desks.