SACRAMENTO, CALIF., JAN. 7 -- Republican Pete Wilson became governor of troubled California today with a vow to introduce an era of "preventive government" despite the worst fiscal crisis in the state's history.

In his inaugural address, Wilson promised that the state would provide prenatal care for every mother in California and pursue programs intended to prevent drug use, learning disorders, school dropouts and gang violence.

"Even in this time of unprecedented fiscal constraint, we must find a way to at least begin to move to a mode of anticipation and prevention," Wilson said.

Ten minutes after he resigned as a U.S. senator, Wilson was sworn in at an upbeat ceremony in the State Capitol that was moved inside hastily when an unusually heavy rain swept the drought-stricken Sacramento Basin.

"See, he's stopped the drought already," a Wilson aide joked.

Despite the lighthearted aside, Wilson and his team have acknowledged that they face grim problems in dealing with a deficit likely to be the largest ever faced by a state.

California, with 29.5 million people, is the nation's most populous state and growing by 800,000 people a year. It also is the nation's largest recipient of foreign immigrants, many of them young and unskilled.

The state's school enrollment is increasing twice as fast as population, and prison confinements by three times population growth.

Last June, the Legislature and then-Gov. George Deukmejian (R) worked out a budget agreement designed to leave the state with a $1 billion reserve when the fiscal year ends next June 30.

Instead, because of the recession and increases in health care, education and prison costs, that surplus now is expected to be a $1.5 billion deficit. Worse yet, the deficit is projected to reach $8 billion by the end of fiscal 1992 unless state spending is curtailed severely.

While Wilson gave no details today, aides said the budget that he will present to the Legislature this week will seek an across-the-board freeze in spending programs and at least temporary suspension of Proposition 98, a 1988 ballot measure earmarking 40 percent of state revenue for education. The measure can be set aside by a two-thirds legislative vote.

"He seeks a balanced program that will spread the pain," said Loren Kaye, Wilson's director of policy development.

This "balanced program" is expected to include tax increases on alcoholic beverages and state fees. But Wilson does not plan to seek income or sales tax increases at this time, although he has said he would consider a sales-tax increase as part of an eventual budget compromise with the Legislature.

California has one of the nation's highest income tax rates and a 6 percent basic sales tax that most urban counties have increased to 7 percent.

Wilson struck an optimistic note today, saying California would overcome the problems of drought, freeze and recession and "will not suffer the future {but} will shape it." He stressed his favorite theme -- that government should focus on prevention rather than remedies for existing problems.

"How much better to provide prenatal care to assure 50 or 60 healthy newborns than to pay for neonatal care for only one unhealthy baby," Wilson said. ". . . How much better prevent learning disorders, than to engage in compensatory education. . . . How much better to prevent crime, than to punish it."

The latter statement is not one likely to have been made by Deukmejian, who took pride in building a record number of prisons in California.

While Wilson paid obligatory tribute to his predecessor and to former governor and president Ronald Reagan today, he also lauded the achievements of the state's two most notable progressive Republican governors of this century, Hiram Johnson and Earl Warren.

He even praised former Democratic governor Edmund G. (Pat) Brown, Reagan's predecessor, calling him "the builder {who} gave California its State Water Project, made deserts bloom and worked to make even greater what is today the world's greatest university system."

Wilson's aides have expressed hope that he will obtain more cooperation from the Democratic-controlled Legislature than did Deukmejian, who prevailed during his eight years by vetoing a record 2,298 bills, all of the vetoes upheld.

Democratic Lt. Gov. Leo McCarthy described Wilson's speech as "very uplifting."

Assemblyman John Vasconcellos of San Jose, the Democratic chairman of the budget-writing Ways and Means Committee, said Wilson "could be a great governor" if he can achieve the goals of his inaugural address. "It's different from Deukmejian. It's a reversal, from minus to positive," Vasconcellos said.

"I give him high marks for his speech and high marks for the thrust of his administration," said Senate Republican Leader Ken Maddy of Fresno.