Not according to the Bible, but according to the Talmud (the central text of Rabbinic Judaism). The Talmud has two components: the Mishnah (dating from about 200 AD or CE) and the Gemara (about 500 AD or CE).
Wikipedia explains: "The time and manner of [Isaiah's] death are not specified in either the Bible or other primary sources. Later Jewish tradition [i.e. the Talmud] says that he suffered martyrdom by being sawn in two under the orders of Manasseh."
Manasseh was the 14th King of Judah, whose story is told in the Old Testament books of Kings and Chronicles. Isaiah, of course, gets a book to himself.
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