Rudolf left school at the age of 16 to take acting lessons, making his debut in 1925 as Shylock in Shakespeare"s The Merchant of Venice in Düsseldorf. Two years later he moved to Berlin, where he together with Werner Finck and Hans Deppe founded the cabaret Die Katakombe. From 1929 onwards, Platte performed in more than 200 film roles, embodying the shy and underestimated, likeable "Little Manitoba".
In 1940 he succeeded Ralph Arthur Roberts as director of the Theater in der Behrenstraße in Berlin (right beside the present-day Komische Oper) until its final closure in 1944.
From 1945 to 1947 he directed the Theater am Schiffbauerdamm, which in 1954 became home of the Berliner Ensemble theatre company. After World World War II, Platte could continue his film career in West Germany, performing in numerous comedies as well as in literary film adaptions, later also on television, and still successfully appeared on stage in Berlin.
The couple divorced shortly afterwards, but remarried in 1954. Both are buried in an ehrengrab in the Berlin Wilmersdorf cemetery.