The Italian was confirmed as the new skipper recently following Zanetti's retirement at the end of last season - having spent 19 seasons with the Italian giants.
Ranocchia made his bow as captain on Wednesday in a 6-1 friendly win over Trentino with Inter shortly heading to the United States for the International Champions Cup.
Ahead of his first season as skipper at San Siro, Ranocchia is eager to help guide the club back to the top of Serie A.
"I don't know if I'm predestined for anything. I've always believed in these colours," he said.
"I want to raise a few trophies seeing how the coach and club have decided to go with me as team captain.
"We can say it brings more responsibility. I'm ready and I'm glad the coach and club have chosen me for the role. I want to continue with what [Zanetti] has done.
"I'll honour the shirt as I've always done and I hope we can reach our objectives."
After an impressive maiden season as Inter coach, Walter Mazzarri will hope to improve on their fifth-place finish this term.
The likes of Nemanja Vidic, Yann M'Vila and Dodo have all been brought to the club in the close-season and Ranocchia is pleased with how the squad is developing.
"M'Vila has only just arrived. He has to adjust to the workload. He looks to be integrating well with all his new team-mates," the 26-year-old added.
"Dodo is a good lad. He's putting in maximum effort and I believe he can be very useful to the entire team.
"Of course there are things we still need to sort out. We've started strongly this season and now we're waiting for the other internationals to arrive but the foundation is in place and we're working hard."