Giannoccaro made his professional racing debut in the 2004 Ferrari Challenge Italy series, finishing thirteenth overall. By 2005 he had transitioned to GT racing under the Scuderia Playteam banner, racing a Ferrari 360 Modena GTC in the Italian GT Championship GT2 class and the Spanish GT Championship. His co-driver in the Spanish series that year was Alessandro Pier Guidi.
The 2006 season was the peak of Giannoccaro's competitive career. Racing a Ferrari 360 GTC for Scuderia Playteam in the Spanish GT Championship, he won the overall title — the series ran as a single class that year, making it an outright championship. The co-driver for this campaign was Alessandro Pier Guidi, and victories came at circuits including Jarama, Valencia, and Estoril.
In the same year Giannoccaro switched to the Maserati MC12 GT1 for the Italian GT Championship, racing under the Scuderia Playteam Sara Free banner with Finnish driver Toni Vilander as co-driver. The pairing dominated the season, scoring twelve victories and two runner-up finishes across eight rounds. The GT1 class title was clinched at Mugello with one round remaining. In Race 1 at Mugello, Vilander built a twenty-three-second lead before handing over to Giannoccaro, who brought the car home first; in Race 2, Giannoccaro fought through from a pit-lane start to third before again exchanging with Vilander, who won.
Giannoccaro also appeared in the FIA GT Championship in 2006, fielding the MC12 at selected rounds. He continued in the FIA GT in 2007, partnering Pier Guidi. Appearances that season included Zolder, where the pair qualified second in class, and the Spa 24 Hours, where a collision late in the race caused retirement close to the finish. At Bucharest the partnership posted competitive lap times. Across eleven FIA GT Championship starts over the two seasons, Giannoccaro recorded no outright race victories in that series, though the team as a whole competed at a high level. In 2007 Scuderia Playteam finished as runner-up in the Italian GT Championship teams' standings.
In 2008 Giannoccaro tested in the Superleague Formula series for the A.C. Milan-affiliated team, the football club-themed single-seater championship. Scuderia Playteam also made appearances that year in the GT Open at Spa-Francorchamps with a Ferrari F430 GTC, marking the wind-down of the team's full-season GT commitments.
Founded in 2003 with the dual purpose of giving Giannoccaro a racing programme and building commercial partnerships, Scuderia Playteam was supported through his Playteam Soleja marketing agency. The team ran Ferrari and Maserati machinery and at its peak competed simultaneously in the Spanish GT Championship, Italian GT Championship, and FIA GT Championship. Sponsors included Sara Assicurazioni, whose name appeared in the team's full title, Scuderia Playteam Sara Free. By 2008 the team's motorsport programme had wound down as Giannoccaro's priorities shifted toward other ventures.
Giannoccaro founded Playteam Soleja, an advertising and sports marketing agency whose clients included BMW, Luxottica, Pirelli, Enel, Sara Assicurazioni, Auchan, and Abarth. Among the agency's productions was the official film for the 2006 Turin Winter Olympics, broadcast during the Opening Ceremony. Between 2004 and 2006 Playteam managed the Italian leg of the Ladies European Tour golf circuit with BMW as title sponsor. The agency also produced a 2008 advertising campaign for the Romanian Government.
In 2012 Giannoccaro and his wife Valentina departed on an extended sailing voyage aboard their Outremer 55 catamaran, visiting the Galapagos Islands, Easter Island, and Patagonia among other destinations. In February 2016 the pair became the first to reach the Antarctic polar circle by catamaran. The voyage ultimately led to Giannoccaro establishing hospitality and adventure tourism ventures in Belize and Guatemala.