Frank is right, in German it had to be spelled with "ö". But let me reiterate: It is not a German song, it is a Yiddish song. In spelling, it is often adapted to German because there is no standard spelling of Yiddish with Latin letters and the original title of the song (בייַ מיר ביסטו שיין where ביסטו is a colloquial contraction of ביסט דו) is hard to read for others.
See
here for the history of the song.