The 18-year-old defenseman, taken with the No. 4 pick of the 2012 NHL Draft, has played for the Western Hockey League team the past two seasons.
"I'm really happy to have the job," Reinhart said, according to the Islanders' website. "I've got to take a bigger leadership role and be more vocal and help the younger guys coming into the league. I've got to lead by example and also communicate with them. I think I'm ready to take a big step up."
Reinhart had 12 goals, 24 assists and a plus-23 rating in 58 regular-season games last season. He added 14 points in 20 playoff games for the Oil Kings, who won the WHL championship.
"He really leads by example out there," alternate captain Travis Ewanyk, an Edmonton Oilers prospect, said. "He's not going to be coming in yelling at guys. You don’t need that, especially when you have a lot of strong voices in there. He proved last year what kind of special player he is."
Reinhart is the fifth captain in Oil Kings history.
"I'm going to try and lead by example -- I think that's the most important thing," Reinhart said, according to the Oilers' website. "But if something needs to be said, I won't be afraid to speak up."
The son of former Philadelphia Flyers goalie Rick St. Croix had 105 points (45 goals, 60 assists) in 72 regular-season games last season. He is the Oil Kings' all-time leading scorer.
"It's a huge honor," St. Croix told the Oilers' website. "I'm going into my fourth year in the Western Hockey League and I'm trying to take on a bigger leadership role this year. In talking with the coaches, they want me to do it. It's something I look forward to and something I'm going to embrace."
The Oil Kings are owned by the same group that owns the Oilers.