The winger is the only Borderer in head coach Gregor Townsend’s starting XV, though fellow ex-Hawick player Rory Sutherland will be on the bench alongside former Melrose and Southern Knights No 8 Rory Darge.
Worcester Warriors loosehead prop Sutherland, 29, and Glasgow Warriors back-row Darge, 22, have both been out injured. The former is currently on 18 caps and the latter on four.
Edinburgh winger Graham, 25, will pick up his 28th cap at the weekend.
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Edinburgh lock Grant Gilchrist replaces Hawick’s Stuart Hogg as captain, the 92-times-capped 30-year-old having been rested for the Scots’ South American tour.
Ex-Melrose player Damien Hoyland is one of five players released following last weekend’s Scotland A victory against Chile. Fellow ex-Melrose men Jamie Bhatti and Rufus McLean retain their places in Townsend’s squad, however, along with Jedburgh’s Glen Young.
Making up the rest of the starting line-up to play the Argentinians at the Estadio 23 de Agosto in Jujuy are Rory Hutchinson, Mark Bennett, Sam Johnson, Duhan van der Merwe, Blair Kinghorn, Ali Price, Pierre Schoeman, George Turner, Zander Fagerson, Jonny Gray, Magnus Bradbury, Luke Crosbie and Matt Fagerson.
Also among Saturday’s replacements are Ewan Ashman, Javan Sebastian, Sam Skinner, Ben White, Ross Thompson and Sione Tuipulotu.
Looking ahead to this weekend’s game, kicking off at 8.10pm and being broadcast live on Sky Sports, ex-Gala and Border Reivers star Townsend, 49, said: “We believe it’s the strongest squad we have available for what will be a very challenging test away from home.
"We’ve got everyone available now apart from Hamish Watson, who picked up a knock around his chest-shoulder area at the end of last week.
“We believe Argentina are one of the strongest teams out there, the equivalent of playing a Six Nations team.
“You're playing away from home against some of the best individuals in club rugby in Europe.
“There are some quality players playing at Edinburgh every couple of weeks, winning championships for Leicester or winning Super Rugby titles for the Crusaders.
“Argentina have always had some brilliant players and they seem to have a great crop just now.”
Explaining his decision to send Hoyland, 28, home, along with Ben Muncaster, Matt Currie, Johnny Matthews and Jamie Hodgson, Townsend added: “Damien was unlucky.
“I think all of them were unlucky because they’ve left a really good impression in terms of how they played and how they trained. It was a tough decision.
“They wanted to stay on tour.
“It would be selfish of us if we kept them a few more weeks because they’ve got pre-seasons with their clubs and the club season will come round very quickly.
“They’ve left a good impression, Damien especially with the three tries. The way he worked in that game shows he can play at test level.
“We hope this experience will drive them through pre-season and into the start of the season with their clubs so they can play test level again come October or November.”