A study of Lyndon B. Johnson provides new evidence that the 36th President stole his first election to the United States Senate, in 1948.

The book, ''Means of Ascent,'' by Robert A. Caro, is the second volume of a projected four-volume study, ''The Years of Lyndon Johnson.'' With a first printing of 250,000 copies, it is to be published on March 15 by Knopf, and excerpts have appeared in The New Yorker.

Mr. Caro maintains that although ballot fraud was common in the late 1940's in some parts of Texas, the Johnson campaign of 1948 raised it to a new level. Mr. Caro supports his charge with an interview with Luis Salas, an election judge in Jim Wells County who said he acknowledged his role only after all others involved in the theft had died.

Determined to Win at All Costs

It has been alleged for years that Johnson captured his Senate seat through fraud, but Mr. Caro goes into great detail to tell how the future President overcame a 20,000-vote deficit to achieve his famous 87-vote victory in the 1948 Democratic runoff primary against a former Governor, Coke Stevenson. A South Texas political boss, George Parr, had manufactured thousands of votes, Mr. Caro found. Johnson died in 1973, Stevenson and Parr in 1975. Mr. Caro says the election showed Johnson's determination to win at all costs as well as his coolness under fire and his ability to select gifted lieutenants, whom he then manipulated.