Born in Schimischow, Weimar Germany (today Szymiszów, Poland), Tschenscher took up refereeing in 1948 and by 1953 he was part of the German Football Association's group of top referees. Within another five years, he was promoted to the FIFA list of international referees. In October 1959, he refereed the second leg of Yugoslavia's 1960 European Nations' Cup first round win over Bulgaria. In September 1962, he took charge of the replay of the 1962 European Cup Winners' Cup Final, in which Atlético Madrid beat Fiorentina 3–0.