The Central Coast Mariners star won his first international cap in a friendly against South Korea last November and is rated is one of the most exciting young talents in the A-League.
A three-match suspension for a rash tackle in an A-League match last month will allow him to travel to Spain to join the Scottish champions in mid-season.
"This is a great opportunity for Tomas to train with Celtic's first team squad," said Mariners general manager of football Lawrie McKinna.
"Celtic are in their mid-season break and are busy preparing for their Champions League matches against Juventus in February, so Tom will undoubtedly learn a lot from the experience."
Rogic earned his call-up for the Socceroos after scoring twice in an A-League match against Sydney FC in early November.
"Technically he is very sound but he has that element of creativity, he does the unexpected, which can decide a game and can give a certain flavour to a game," Australia coach Holger Osiek said at the time.
"That is what I like, he is not an average player. Physically he has to mature, his endurance capacity has to improve and his mobility in tight areas needs to get better.
"That will come with time and will be achieved but what you can't achieve is natural talent."