Rambaudi gained Serie A promotion with Foggia after winning the 1990–91 Serie B title, forming a notable attacking trio with Giuseppe Signori and Francesco Baiano, helping the team to a ninth-place finish in Serie A during the 1991–92 season under manager Zdeněk Zeman. He later moved to Atalanta during the summer of 1992, where he remained for two seasons. After the club were relegated in 1994, he moved to Lazio, alongside his former manager Zeman, where he put on notable performances, earning a call-up to the Italian national team. He later moved to Serie B sides Genoa, and later Treviso, before ending his career in 2000 in Serie B. Overall throughout out his 16-year club career, he made 411 appearances, scoring 82 goals, between 1984 and 2000.