Horowitz, baseball, biking . . .; Life of a 1920s fan club idol Horowitz, by Glenn Plaskin. New York: William Morrow & Co. 607 pp. $19.95.

Volodya Gorovitz/ Makes girls have fits./ All of them are wild/ About his piano style!m In the early 1920s, this bit of doggerel was chanted through the streets of Leningrad by members of a teen-age fan club. It presaged the worldwide fame and adulation soon attached to the pianist's name under a slightly different spelling: Vladimir Horowitz.

Biographer Glenn Plaskin follows Horowitz from his musical debut in Russia to his Golden Jubilee concerts in America more than 50 years later - still critically acclaimed for ''massive sonorities, tremendous (though no longer infallible) technique, penetrating tone and musical electricity.''

In this first-ever book on his life, Horowitz emerges much less appealingly as a person than as an artist. Plaskin describes him as an ''introverted, thoroughly spoiled eighteen-year-old'' who grew into an adult disliked by many for his ''fits of temperament, his selfishness, and his boundless ego.''

Until now, Plaskin notes, ''many of the essential facts of biography have been ignored: an accurate itinerary of Horowitz's activities, a detailed description of his personal character and relationships to his family and friends; a systematic discussion of his repertory, his musical style, and the impact of his playing on younger pianists.'' Plaskin supplies all these elements with objectivity and sensitivity. A fine performance.