The event took place on the 75th anniversary of D-Day. Cardona was promoted from lieutenant junior grade.
"Congratulations to Lieutenant Joe Cardona on his promotion," said Patriots coach Bill Belichick, whose father coached for 33 years at the Naval Academy. "And obviously a day to remember our World War II veterans on D-Day. The 75th anniversary, that's kind of a big one for us. I want to recognize all the things that they did."
It was a special moment for Cardona, who has spent his four-year NFL career balancing his football and active-duty commitments, including time in nearby Rhode Island at the Naval Preparatory Academy.
"It's pretty emotional when you see someone take the oath like that and raise his hand," quarterback Tom Brady said. "It's a big commitment Joe's made, and I think Joe has done it very proudly and does a great job educating a lot of us on what it means to him. I think we all appreciate that.
"We see the work he does here for us, but also the work he does for our country. I've talked to Joe a lot over the years about what his roles and responsibility are and I think everyone is proud of his accomplishments."
The 27-year-old Cardona, selected by the Patriots in the fifth round of the 2015 NFL draft, has never missed a game in his career, joining Dallas Cowboys quarterback Roger Staubach as the only graduates of the Naval Academy to win multiple Super Bowls.
"As proud as you are of winning a Super Bowl ring, to advance in that part of his career is pretty amazing," Brady said. "To do both is really a great thing for him personally. It was nice to be able to celebrate and congratulate with him."
Cardona, whose father also served in the Navy, has been a reliable player for the Patriots and someone admired by Belichick.
"[We're] happy to recognize Joe on this day," Belichick said. "It just makes it a special day for all of us."
ESPN's Mike Reiss contributed to this report.