The 37-year-old, who is currently technical and performance adviser at Chelsea, retired from professional football at the end of last season.
Cech trained with another ice hockey side, the Guildford Flames, earlier this year and the former Czech Republic international has since joined the Phoenix as a goaltender.
“I am delighted to have the opportunity to play with the Phoenix to get match experience,” Cech said in a statement on the club’s website.
“I hope I can help this young team to achieve their goals for the season and try to win as many games as possible when I have the chance to play.
“After 20 years of professional football this is going to be a wonderful experience for me to play the game I loved to watch and play as a kid.”