He graduated with an abitur from the gymnasium in Ludwigslust. He studied mathematics and physics at the Humboldt University in East Berlin (German Democratic Republic), and there in 1963 Rautenberg received a doctorate and worked as a logician.
In 1968 Rautenberg graduated from the Humboldt University as an academic lecturer. From 1969 to 1973 Rautenberg was docent at the Humboldt University. Because the Stasi contacted him to force him into co-operation, Rautenberg left East Germany in 1973 and in 1974 became Professor in West Germany.
In 1976 he accepted a call to chair the academic department for mathematical logic and foundations of mathematics at Freie Universität Berlin.