Peter Randt was on the East German handball team at the 1972 München Olympics that unfortunately lost the bronze medal match, 19-16, against Romania. He earned 12 international caps. Domestically, he played with SC Empor Rostock and then SC DHfK Leipzig. With Leipzig, he won the European Champions Cup in 1966. Randt started a coaching career after his playing retirement that lasted until German re-unification. He then moved to Bad Säckingen, working as a physiotherapist in a rehabilitation clinic.