Born in Tashkent, Uzbekistan, Borok studied violin in Riga, Latvia, with Voldemar Sturestep.
Borok won top prizes in the All-Russian Republic and All-Soviet Union violin competitions.
In 1974, Borok emigrated to the United States, to take the post of associate concertmaster of the Boston Symphony Orchestra.
In 2013, he joined the violin faculty at the Meadows School of the Arts of Southern Methodist University as an artist-in-residence.
His survivors include his wife Marilyn, his ex-wife Zinaida, and their two children, Mark and Sarah.