He will provide front row cover for the remaining games of the tournament.
Gordon, who is the 14th Glasgow player to join the squad, flew out to South Africa just hours after hooker Fraser Brown.
As well as the players away with Scotland, Stuart Hogg, Sean Maitland and Ryan Grant are in Australia with the British & Irish Lions and seven Scotstoun-based players are at the IRB Junior World Championship in France with the Scotland U20s.
The Scotland team to face South Africa on Saturday is due to be named tomorrow.
Gordon said: "It's really good to be called up to the summer tour. I was halfway through a training session with Glasgow when I got the call. I was really surprised but I'm excited about the chance this gives me."