Fred Ebb wrote the lyrics for this song and John Kander composed the music for their 1966 musical
Cabaret.
It was then, of course, not the anthem of the National Socialists. This was actually the Horst Wessel lied (also called Die Fahne hoch), which, if we want to talk about films, was used throughout Leni Riefenstahl's 1934 film Triumph of the Will (Triumph des Willens).
As most people are more aware of the appearance of the song in the film version (well described above by ArsDuo) rather than the play, I've done some research about how it is used there.
In Act I of the musical, the Master of Ceremonies of the Kit Kat Club comes out on stage with a record player and starts losing himself in the song a boy soprano is singing. At the end, the Master of Ceremonies turns off the music and announces "To me!"
The song is reprised as the finale of Act I at Fraulein Schneider and Herr Schultz's engagement party. Herr Ludwig arrives late, and is quite pleasant to Schultz. When Ludwig removes his coat, his Nazi armband is seen. Cliff gets angry, and Fraulein Kost lets slip that Herr Schultz is a Jew. Ludwig tries to leave. Kost stops him, and leads him and almost the whole party in the song.
Thanks to Phyllis Stein for some help.