Manager Martin O'Neill has included the uncapped duo in a 27-man squad for the trip to Glasgow on Friday and a friendly against the United States next Tuesday.
The European Championship qualifier gives Ireland the chance to maintain their unbeaten start in Group D and a victory would see them open up a six-point lead over their hosts.
Christie has impressed at right-back for Derby County this season as they have climbed to the top of the table, while striker McGoldrick has struck five times in the second tier of English football for Ipswich Town.
Stoke City defender Marc Wilson is ruled out, and also misses the friendly against the United States next week, after suffering a hamstring injury against Tottenham on Sunday.
Everton midfielder James McCarthy will be assessed prior to the Scotland encounter after he also sustained a hamstring problem against Sunderland on Sunday.
Squad in full:
Goalkeepers: Rob Elliot (Newcastle United), David Forde (Millwall), Shay Given (Aston Villa), Darren Randolph (Birmingham City)
Defenders: Cyrus Christie (Derby County), Ciaran Clark (Aston Villa), Seamus Coleman (Everton), Richard Keogh (Derby County), John O'Shea (Sunderland), Alex Pearce (Reading), Stephen Ward (Burnley)
Midfielders: Robbie Brady (Hull City), Darron Gibson (Everton), Jeff Hendrick (Derby County), James McCarthy (Everton), James McClean (Wigan Athletic), Aiden McGeady (Everton), David Meyler (Hull City), Anthony Pilkington (Cardiff City), Stephen Quinn (Hull City)
Forwards: Kevin Doyle (Crystal Palace), Robbie Keane (LA Galaxy), Shane Long (Southampton), Daryl Murphy, David McGoldrick (both Ipswich Town), Anthony Stokes (Celtic), Jonathan Walters (Stoke City)
