The Polish goalkeeper has rejoined the Giallorossi on a season-long loan from Arsenal and is intent on helping the capital club push for the Italian premiership having finished third last term.
Roma have not triumphed since 2001 but Szczesny wants to maintain a positive outlook as they prepare for the impending campaign under Luciano Spalletti.
"Do I have a message to the fans? Just keep believing," Szczesny told Roma TV after penning a new 12-month deal.
"We showed you guys what we can do last year and I'm sure that we can continue that this year throughout the season.
"With your belief behind us, I'm sure we can achieve great things."
The 26-year-old added: "I've joined AS Roma and I want to win the Scudetto.
"That's the only objective I have. I think we had a good second half of the season last year, but when you play for a big club you have to fight to win the titles."