[3] On 7 November 1976, being 15 years and 9 months old, Geolgău made his Divizia A debut under coach Constantin Teașcă, playing for Universitatea Craiova in a 3–1 victory against UTA Arad.

[6][7] Geolgău went on to play 13+1⁄2 seasons with Universitatea Craiova, being part of the "Craiova Maxima" generation, helping them win two consecutive league titles in 1980 and 1981, at the first he was used by coach Valentin Stănescu in 24 games in which he scored two goals and at the second coach Ion Oblemenco gave him 29 appearances in which he scored three goals.

[3][9] After one season spent in Cyprus, he went to play for one year at Belgian side Avenir Lembeek, returning to Romania where he retired at Jiul Craiova.

Ion Geolgău played for Romania in 23 matches, scoring three goals, making his debut on 10 September 1980 when coach Valentin Stănescu sent him on the field in the 60th minute to replace Tudorel Stoica in a friendly which ended with a 2–1 away victory against Bulgaria, which took place in Varna on the Yuri Gagarin Stadium.

[1][12][13] Geolgău also played three matches at the 1986 World Cup qualifiers, scoring one goal in a 3–2 loss against Northern Ireland.