Giugliano played for ACFD Pordenone before joining ASD Torres Calcio in 2014. The following year she signed for ASD Mozzanica. In the summer of 2016, Giugliano agreed to move abroad and play for Primera Iberdrola side Atletico Madrid but then reversed her decision to move to Spain for personal reasons. On 22 September 2016, she returned to her native Italy to sign for AGSM Verona. She then joined ACF Brescia in 2017 before moving to Milan the next season as part of Milan's acquisition of Brescia's Serie A license.
