As a youth Czibor played for Komárom AC and Komárom MÁV and was working as a train engine driver before he was noticed by Sándor Mezei, the coach of the Hungary youth team. He subsequently played for Ferencváros TC where he won his first Hungarian League title in 1949. After a spell with Csepel SC he conscripted into the army team, Honvéd. During his playing career in Hungarian club football, Czibor scored 100 goals in 175 matches.
In 1953, Czibor joined Honvéd where his team mates included fellow internationals Puskás, Kocsis, and Bozsik. During his time at the club he won a further two Hungarian League titles in 1954 and 1955. He finished 1955 as top goalscorer in the league after scoring 20 goals. In 1956, Honvéd FC entered the European Cup and in the first round they were drawn against Athletic Bilbao. Honvéd FC lost the away leg 2–3, but before the home leg could be played, the Hungarian Revolution had erupted back in Budapest. The players decided against going back to Hungary and arranged for the return with Athletic to be played at the Heysel Stadium in Brussels. However, early in the game, the Honvéd FC goalkeeper was injured and, with no substitutes permitted, Czibor had to go into goal. Despite drawing 3–3 they went out on 6–5 on aggregate. Elimination left Honvéd in limbo. The players summoned their families from Budapest and, despite opposition from FIFA and the Hungarian football authorities, they organised a fundraising tour of Italy, Portugal, Spain and Brazil. After returning to Europe, the players parted ways. Some, including Bozsik, returned to Hungary while others, including Czibor, Kocsis and Puskás, found new clubs in Western Europe.
FC Barcelona
Czibor initially went to Italy and played a couple of unofficial games for AS Roma before another Hungarian refugee, Ladislao Kubala, persuaded him and Sándor Kocsis to join him at FC Barcelona where he became a vital member to the team. He subsequently scored on his La Liga debut in a 6–0 win over Valencia CF and as part of a team that also included Ramallets, Evaristo and Luis Suárez, Czibor won a Copa del Generalísimo/La Liga double in 1959 and a La Liga/Fairs Cup double in 1960. Although he did not play in the Copa final, he scored twice in the Fairs Cup final as CF Barcelona beat Birmingham City 4–2. CF Barcelona and Czibor also reached the final of the European Cup in 1961, where Barcelona lost 3–2 to Portuguese club S.L. Benfica.
Later career
After three seasons at Barcelona, he joined their local rivals Español for the 1961/62 season. He had brief spells in Switzerland with FC Basel, and in Austria with FK Austria Wien. In 1964 he played in the Eastern Canada Professional Soccer League with Hamilton Primo FC.
