Czibor played as a left-winger or striker and was notable for having a powerful shot, good pace and excellent ball control.

After the 1956 Hungarian Revolution he moved to Spain where he became a prominent member of the successful FC Barcelona team of the late 1950s.

Together with Ferenc Puskás, Sándor Kocsis, József Bozsik and Nándor Hidegkuti, he formed the nucleus of the Golden Team that went unbeaten for 32 consecutive games.

In 1953, Czibor joined Honvéd where his teammates included fellow internationals Puskás, Kocsis, and Bozsik.

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.

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.

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.