The 20-year-old, who operates in attack like his father, has joined the Lombardy-based side after spells in the Chelsea youth setup and with the Under-19 and B teams of French side Guingamp.
Isaac will be tasked with firing his new employers towards Serie C, as they currently sit seventh in Group A of Serie D, two points outside a playoff spot.
The 20-year-old mainly operates as a central striker, but can also play on the left and the right of a front three.
Prior to joining Folgore Caratese the younger Drogba had been without a club since leaving Guingamp's B side last summer.
His deal with the Italian side runs until June 30.