Tzur was born Ze'ev Stein on 11 September 1911 in Krynki, Russian Empire (now in Poland) and studied at a Hebrew gymnasium in Hrodna, before attending a polytechnic in Vilnius, and was a member of the youth movement of the Polish Social Zionists and Dror.

He was elected to the Knesset on the Ahdut HaAvoda list in 1955, and on 5 December that year was appointed Deputy Minister of Agriculture.

The following year he became a member of the editorial board of LaMerhav, the party's newspaper, on which he sat until 1969.

He returned to the Knesset on the Alignment list (an alliance of Ahdut HaAvoda and Mapai) in 1965, and in 1968 became a member of the central committee of the newly formed Labor Party.

He lost his seat again in the 1969 elections, and later served as a director of the Tabenkin Centre.