The Newcastle flanker was born in Stirling and is the son of former Scotland prop George Graham.
He is one of eight uncapped players in Eddie Jones’ 35-man squad but there is no place for another ex-Scotland U20 international, scrum-half Ben Vellacott.
Instead, the Gloucester scrum-half is included in England’s 45-man Elite Player Squad (EPS).
But there is a place in the Six Nations pool for Bath back row Zach Mercer, a former Scotland U16 international.
Scotland coach Gregor Townsend spoke on Tuesday about losing Graham and Vellacott to England.
“It’s unfortunate timing for us. England had a [training] squad in the first week of January and they put Gary in it,” Townsend said.
“Gary is a Scotland U20s player and someone we have been impressed with since he got into the Newcastle team.
“But given he has been picked in that England squad, I can understand why he wants to see where that leads.
“We will wait and see. If England play him during the Six Nations he will obviously be committed to England. It seems England are very keen on him.”
Speaking about Vellacott, Townsend said: “Ben is someone we have talked to a lot over the last couple of seasons. I almost signed him at Glasgow. He came up for a couple of days but decided to stay at Gloucester.
“We have been in regular communication with him but again we will wait and see what squad England pick in the next couple of days but it looks likely he will be involved with them in the Six Nations.”
A succession of injuries and suspensions - including to star players Billy Vunipola, Elliot Daly and Nathan Hughes - have forced Jones to bring in a host of new faces.
Saracens wing Nathan Earle, Northampton centre Harry Mallinder and Harlequins full-back Marcus Smith are the rookie backs included.
Exeter prop Alec Hepburn, Harlequins prop Lewis Boyce, Newcastle flanker Graham, Bath back row Mercer and Bath hooker Tom Dunn make up the new faces in the forwards.
“I’ve selected the strongest available squad to prepare for our opening match against Italy,” said Jones, who on Wednesday signed a contract extension until 2021.
“It’s important we start the tournament well and we will spend the next two weeks training smart and really fine-tuning our gameplan for the Italy match next month.
“I’m expecting a really positive training camp in Portugal and while we have a few players unavailable through injury or suspension, it has provided opportunity for others who will be desperate to be involved in the Italy game.”