Röthke studied theology, but decided to change studies, instead graduating with a doctorate of law from the University of Berlin. During the German occupation of France, he was initially in Brest, where he worked as a Kriegsverwaltungsrat ("military administration counselor"), before becoming the deputy to Theodor Dannecker in spring 1942 and succeeded Dannecker as the Chief of the Department of Jewish Affairs in France (in Paris) for the Eichmannreferat in July of the same year. Röthke served in this role until August 1944. His assistants were Ernst Heinrichsohn and Horst Ahnert. His active role in the deportations of Jews to Auschwitz was teletyped on 5 November 1942 to the RSHA:
German: Am 5.11.1942 wurden in Paris 1100 Juden griechischer Staatsangehörigkeit festgenommen. Infolgedessen wird es notwendig, daß noch ein vierter Transport am Mittwoch, den 11.11.1942 nach Auschwitz abgeht.
English: On 5.11.1942, 1100 Greek Jews were arrested in Paris. Consequently, it is necessary that a fourth transport on Wednesday, 11.11.1942, go to Auschwitz.
After the war, Röthke lived in Wolfsburg, where he worked unmolested as a legal counsel. In October 1961, he received a monthly pension from the Free State of Bavaria. Röthke died in July 1966 in Wolfsburg. According to Serge Klarsfeld, Röthke was convicted in 1945 in France and sentenced to death in absentia.