Rotenstreich was born in 1914 in Sambir, Galicia, then in the Austria-Hungary, later in Poland, now in Ukraine. His father, Ephraim Fischel Rotenstreich, was a Zionist leader. In 1932, Rotenstreich emigrated to Mandate Palestine.
Rotenstreich studied philosophy at the Hebrew University of Jerusalem, obtaining bachelors and masters degrees and a PhD. He joined the faculty in 1949 and served as rector of the university from 1965 to 1969. He was a member of the Israel Academy of Sciences and Humanities from 1959.
In 1973, he was appointed Chairman of the Planning and Budgeting Committee of the Council for Higher Education in Israel, and was one of the early members of the Israel Academy of Sciences and Humanities. He was a member of the central institutions of the Mapai movement.