He played mainly as a centre-back despite being only 1.80 m in a career that lasted 20 years, and made 112 appearances at international level, being Switzerland national team's fifth most capped player.
He helped the club win the 1984 Swiss Cup, defeating Lausanne Sports 1–0 after extra time in the final, and the league title in 1985.
An aspiring Neuchâtel Xamax side acquired his services in 1986, and he helped it win the national championship during the only two seasons he played for them, 1986–87 and 1987–88.
In 1995, Geiger signed for Grasshoppers, where he finishing his career after a further two seasons, having played 496 Swiss first division matches, with 38 goals.
Geiger made his international debut in Switzerland's 2–1 defeat to England at Wembley Stadium, on 19 November 1980, and went on to be capped 112 times and score five goals, between 1980 and 1996.
He captained his country at both this competition and the 1994 FIFA World Cup in the United States, usually being accompanied at centre-back by Dominique Herr.
Subsequently, Geiger had short spells managing Neuchâtel Xamax, FC Aarau and Lausanne Sports before being given the job at Botola side Olympique Safi in 2006.