Building up the excitement, the 33-year-old actress announced the title on her Twitter page.
She plays the lead role of Alex Parish, an FBI agent on the thriller series, which marks her debut on American television.
"The name of the 1st episode of #Quantico is "Run." Can't wait for you to run to your TV on Sept 27 for @QuanticoTV!" tweeted the "Mary Kom" actress.
On being asked by a fan about the Indian premiere date, Priyanka replied, "October 3 onwards."
Star Network will telecast "Quantico" as part of its prime-time line-up on Star World and Star World HD in India immediately after the US telecast.