Back-row Courtney Lawes (33), England's most recent skipper, has been ruled out of this weekend's match with concussion.
Inside centre Farrell has been passed fit following a concussion suffered while playing for Saracens and takes his place in an England midfield featuring fly-half Marcus Smith (23) and powerhouse outside centre Manu Tuilagi (31), whose Test career has been blighted by injury.
It is the first time the trio have been selected to play together for England.
Farrell last captained England against Australia in November last year, when he suffered an ankle injury.
He then sustained another ankle injury that kept him out of the 2022 Six Nations, with Lawes and Tom Curry (24) leading England in the championship.
Farrell returned for England's victorious tour of Australia in July, when Lawes was captain.
England coach Eddie Jones has recalled wing Joe Cokanasiga (24) and scrum-half Ben Youngs (33), with the veteran Australian boss giving an international debut to Northampton lock Alex Coles (23).
Coles will make his debut in the second row alongside Jonny Hill (28) while Maro Itoje (28) makes his first appearance at blindside flanker since Italy were defeated in February.
"It's been a really good week of preparation and I've been very pleased with the squad's attitude," said Jones. "They've shown real work ethic and a determination to improve.
"We're looking forward to a great game of rugby at a full Twickenham Stadium against a very good Argentina side."
Following the match against the Pumas, England face Japan, New Zealand and world champions South Africa on successive weekends at Twickenham.
England team (15-1) to play Argentina at Twickenham on Sunday (kick-off 1415 GMT):
Freddie Steward; Jack Nowell, Manu Tuilagi, Owen Farrell (capt), Joe Cokanasiga; Marcus Smith, Ben Youngs; Billy Vunipola, Tom Curry, Maro Itoje; Jonny Hill, Alex Coles; Kyle Sinckler, Luke Cowan-Dickie, Ellis Genge
Replacements: Jack Singleton, Mako Vunipola, Joe Heyes, David Ribbans, Sam Simmonds, Jack Willis, Jack van Poortvliet, Henry Slade
Coach: Eddie Jones (AUS)
