Considered to be one of the best rural cyclists of his day, Józef Beker began his competitive career when he was 20-years-old. In 1961 Beker became the Polish champion in the team road race, winning his first stage of the Tour de Pologne in the same year. During the next edition of the race he had six top-10 finishes to place sixth overall in the general classification. Beker continued with his good form at home, in addition winning the seventh stage at the Tour of Bulgaria in 1963. His consistent results earned him a place on the Polish Olympic team for the 1964 Games in Tokyo, where he came 11th in the 100 kilometres team time trial. Beker had the best result of his career one year later when he won the Tour de Pologne. He won a further stage of the race in 1966, along with winning the 12th stage of the Milk Race in England.
Poland