The American, who last drove for the Hingham-based team at the Young Driver Test at Yas Marina last year, will stand in for Heikki Kovalainen.
Speaking about his opportunity, Rossi said: "I am looking forward to getting back into the F1 car in Spain and I want to thank the team for the chance to run in FP1 in Barcelona.
"I have a clear goal for the session - make sure I run to the plan set by the engineers, not make any mistakes and learn as much as I can over the whole weekend."
Rossi's only other F1 experience came at the end of 2009. He was given a run by BMW Sauber when the young driver test was held at Jerez.