Anton played for the Chelsea youth team and was dressed in Hoops training gear as he took his place alongside new signing Jonny Hayes and star forward Moussa Dembele on the flight.
The 24-year-old is currently without a club after his contract ran out at Swindon and was spotted at Lennoxtown last week.
Anton has also turned out for Brighton and Oldham during his career so far.
His dad Brendan went to watch him in action when Swindon took on Charlton last November.
The Treble winners are preparing for their Champions League qualifying campaign with a series of friendly fixtures.
They take on BW Linz and SK Rapid Vienna before heading to the Czech Republic to face Slavia Prague.
Celtic finish off their round of warm-up games in Ireland with a match against Shamrock Rovers before going up against either Linfield or La Fiorita in the Champions League second qualifying round.