President Carter formally tapped Texan John C. White yesterday as his choice for Democratic national chairman and told him he had "a free hand" to make any changes he wants at the Democratic National Committee.

White, 53, said he would leave his present position as deputy secretary of argiculture as soon as his selection is ratified by the DNC members - who will meet in Washington on Jan. 27 or Feb. 3 for the purpose.

"I always thought it was foolish to resign before you're on another payroll," said the man who served for 26 years as Texas commissioner of agriculture before coming to Washington last March.

White met at the White House yesterday morning with Carter and out-going DNC Chairman Kenneth B. Cutis, the former Maine Governor who struggled with the party's carryover debts and fussing factions for 12 frustrating months.

They both did their best to put a bright face on the picture, with Curtis saying he "enjoyed it very much" and White saying his predecessor had assured him it was "beautiful job."

In turning the party chairmanship over to White. Carter hoped to find the same sort of healing balm supplied by White's fellow-Texan and close friend Robert S. Strauss, who ran the national committee from 1973 through 1976.

White, unlike Curtis, was not an early Carter backer, supporting instead the favorite-son candidacy of Sen. Lloyd M. Bentsen Jr. (D-Tex.). But he helped carry Texas for Carter in the general election.

Yesterday, he left no doubt about where his loyalities lie, saying he would be "fair" to anyone who may challenge Carter for renomination in 1980 but specifying "certainly I support him [Carter] if he chooses to run."

White apparently gained at the outset one power Curtis lacked as national Chairman - the right to staff the DNC entirely with his own choices.

"I asked for a free hand," White said, "and he [Carter] said I had it."

The new chairman has survived three decades of Texas political infighting with his sense of humor intact.

Asked at a press conference why he thought he had been chosen, he said, "Somebody told me they needed a lyin', double-crossin' SOB in there, but I hope that's not the reason . . . I think it's because I'll bring the same low-key, sophisticated, educated, genteel spirit to the position as Bob Strauss did."

The qualities the President stressed in telegrams to national committee members in which he recommended White were that "through thick and thin, John White has been a loyal and dedicated Democrat - a talented organizer, an articulate spokesman, a tough and fair leader."

White proved his loyalty early in his career, in 1952. Alone among statewide elected officials, he refused to follow the lead of then-Gov. Allan Shivers (D) in supporting Republican Dwight D. Eisenhower for President and cross-filing for office on both Republican and Democratic tickets.

Twenty years later, in 1972, when few other Texas Democrats were willing to identify themselves with the presidential candidacy of Sen. George S. McGovern (D-S.D.), White took on the task of managing McGovern's Texas campaign.

Calling himself a political "modernate," he noted yesterday that he had supported the "reform" effort to apply proportional representation, rather than winner-take-all rules, to the selection of Democratic convention delegates in 1976.