The 22-year-old, whose first year at Anfield has been marred by injuries, was ruled out for the rest of the season after dislocating the joint in February.
Borini, a £10.5m signing from Roma last summer, had already missed three months earlier in the campaign with a broken foot.
He wrote on Twitter: "Today first full training after injury!!! #firstraining #back #happy."
Borini has scored one goal in 16 appearances since joining the Reds.