After engagements at the opera of Tel Aviv and at the Yemenite theatre INBAL, Röthler finished his degree at the conservatories in Cologne and Berlin in 1963. In Berlin he worked as a music therapist at the psychiatric clinic. In 1968 he started teaching at the Mozarteum Salzburg. In 1981 he was appointed to a professorship for cembalo/harpsichord and music theory.
In 1983, Röthler translated the book Playing the Harpsichord. He died in Salzburg.