James S. Rosebush, a 32-year-old presidential assistant in charge of encouraging the private sector to support social programs, was appointed as Nancy Reagan's staff director yesterday. He replaces Peter McCoy, who left the East Wing to become under secretary of commerce for travel and tourism.

Rosebush was selected by White House deputy chief of staff Michael K. Deaver, a former public relations man who is said to be impressed with Rosebush's promotional ability. Nancy Reagan interviewed him Thursday. He begins his job Feb. 1.

Rosebush would give no press interviews yesterday, but he did provide a picture of himself. "In front of an American flag," said one amused East Wing official. Few on Nancy Reagan's staff know him, although yesterday he came through their offices to say hello.

"He's a very nice young man," said Sheila Tate, Nancy Reagan's press secretary. "I don't know much about him."

Privately, several senior administration aides expressed surprise that Rosebush was the choice for the job. In the less-than-generous way of White House aides, two officials separately referred to him as "pompous," and one said his promotional ability was perhaps best exercised on himself.

But presidential assistant Richard Darman remarked: "Mrs. Reagan has a strong interest in the private sector initiative program, and Jim has been creative in developing that program. For this, and many other reasons, he's an excellent choice."

"He came in here, and with literally no staff, handled a major policy area," said Craig Fuller, a presidential assistant and social friend of Rosebush's. "If there's any dislike of him out there, it's some sort of jealousy. He's very personable."

"I am happy and pleased that Mrs. Reagan has selected someone who will be a benefit to her staff," said one official. "God, they'll hate him."

Rosebush would not respond to these remarks. "I have given him every message," said his secretary when told of them, "and he's instructed me to say that he will not give any press interviews at this time."

A native of Flint, Mich., Rosebush graduated from Principia College in Elsah, Ill., later receiving his master's degree in public affairs from Boston University. Since August 1981, Rosebush has been a special assistant to the president in charge of the White House private sector initiative program. He joined the administration in May 1981, as director of the office of business liaison at the Commerce Department.

Before that, he was in charge of a $10-million corporate contributions program for Standard Oil of Ohio. And before that, he was a vice president for the National Chamber Foundation, a public-policy research group, and Citizens Choice, a national taxpayers' lobby. Both are part of the U.S. Chamber of Commerce. He and his wife, Nancy, have two children. They live in Washington.

Rosebush, a trim, finely tailored man, was described by several women at the White House yesterday as "handsome." Insiders say he is a good choice for Nancy Reagan. He will oversee a staff of 13 and an approximately $600,000 annual budget. His salary will be somewhere under $56,000, the same earnings that McCoy received. He will run the day-to-day operations of the office, including scheduling, assessing the seating at state dinners, advising Nancy Reagan on public remarks and -- as was the case with McCoy, at least -- carrying the first lady's purse.

In the weeks before Feb. 1, presidential assistant Joseph Canzeri will continue to fill in, as he has done since McCoy left in December.