The 18-year-old makes the move across the English Channel having been scouted in the Combined Counties League, where he played seven games for Guernsey.
He said: "It's a dream come true. I've worked really hard to get my chance and I'm delighted to have been given this opportunity to play football at such a high level.
"I want to do all I can to grow as a player and hopefully I'll be pushing to be involved with the first team in the future."
A former New Zealand Under-17 international, Jordan has signed a deal keeping him at Ashton Gate until the summer.