Born in Rome, Giannini began his career as a youngster with local club Almas Roma. From a young age he attracted the attention of many of Italy's clubs, eventually signing with Roma ahead of rivals including S.S. Lazio and A.C. Milan. He made his Serie A debut on 31 January 1982 in a 1–0 defeat to A.C. Cesena and went on to make over 400 appearances for the club over the following fifteen years. During his time at Roma, whom he went on to captain, he won the Serie A title once, and the Coppa Italia three times; he also played in the UEFA Cup final during the 1990–91 season, although he did not take part in Roma's run to the 1984 European Cup final.