The 35-year-old was available on a free transfer after leaving the Swans during the summer, ending an 11-year stay at the Liberty Stadium which saw him start in League One and spend seven seasons in the Premier League.
Rangel has now penned a five-month contract with QPR which will keep him at the club until January 13, following an injury to Darnell Furlong which is expected to keep him out for three months.
"I had a phone call from the manager saying he was looking for some experience. I think the main word used was experience. He wants to use my Premier League experience as an important part of our game," Rangel told the club's official website.
"I want to use every single weapon I have to help the team achieve their targets. I've seen lots of talent in training - from what I have seen we can only get better.
"I know I am not 20 anymore but when you have been in the British game for so long, you gain experience and I think that's what I can contribute day in, day out. I am delighted to be here and I hope I can help as much as I can."
Manager Steve McClaren added: "We invited him in 10 days ago to train. He's had 11 years at Swansea City in the Championship and Premier League, so he comes with great experience.
"He's a very good professional and a very good person, and that was one of the main things we wanted in the dressing room. We hope Darnell will come back in three months. Ossie Kakay is obviously still learning the game and young, and we needed someone with experience and professionalism. Angel came in and demonstrated that in bags.
"All the players can benefit tremendously from having him around. When you see him train, you know he has a pedigree and I am delighted to have him here."
Rangel, who will wear the number 22 shirt at Loftus Road, could make his debut away to West Bromwich Albion on Saturday.