No, Elvis Presley was not a Jew.
Wikipedia reports that, "The family attended an Assembly of God church, where he found his initial musical inspiration. Presley's ancestry was primarily a Western European mix: on his mother's side, he was Scots-Irish, with some French Norman; one of Gladys' great-great-grandmothers was Cherokee. Presley's father's forebears were of Scottish and German origin."
A Cantor who lived above the teenaged Elvis in Memphis recalls the Elvis at times was his Shabbos Goy - that is, he turned on lights for the Orthodox man who would not do that on the Sabbath. [Hat tip to Barak!]
The interview with the cantor was done by KCRW.
They summed it up: "The story of an orthodox Jewish family who lived above Elvis Presley’s family in a house in Memphis. They would often call on teenage Elvis to be their Shabbos Goy - the gentile who would perform "work" that religious Jews did not do while on the Sabbath or day of rest. In return, the Fruchter’s may have unwittingly influenced Elvis’ music."