In August 1967, Sivan joined the Israel Defense Forces and became a coding instructor in the signals corps at Tzrifin.

His thesis focused on "Northwest Semitic in Akkadian texts from Ugarit" and was under the guidance of Professor Anson Frank Rainey.

He was a member of the band "Koah Meshikha" (Gravity) in which he played the guitar and sang blues and jazz songs with his brother, Gabi Siboni.

In October 1979 he was appointed a lecturer in the Department of Hebrew Language at Ben-Gurion University of the Negev, and in 1997 he became a full professor.

Between 2000 and 2004, Sivan held the position of Head of the Department of Hebrew Language and functioned as the Vice-Dean of the Faculty of Humanities and Social Sciences during the tenure of Dean Jimmy Weinblatt.

In 1995, together with Professor Haim Cohen, Sivan received an Honorary Award on behalf of the Israel Science Foundation.