Mr Ranger admitted having sex with the woman but said it was consensual.
After the foreman delivered the not guilty verdict Mr Ranger banged on the sides of the dock and said: "Thank God for that."
As he walked out he thanked the jury and pulling off his tie said: "What a joke."
Dismissing the jury, Judge Evans thanked them for their consideration.
Mr Ranger made no comment leaving the court but his solicitor, Geoffrey Forrester, said he was "delighted" with the result.
"It took the jury approximately one hour, after hearing evidence extending over seven days, to find him not guilty," he said.
"He's obviously delighted with the result and wants to get back to doing what he does, playing football, and he just wants to get on with his life."
During the trial the jury heard about trouble that Mr Ranger had been in previously.
This included serving an 11-week sentence in a young offenders' institution when he was just 15 after he took part in a street robbery. Growing up in North London, he mixed with an older gang, and also had convictions for burglary and handling stolen goods back in 2007.
Writing on Twitter, Ranger said: "I would like to take this opportunity to thank everyone involved. My legal team, my family and everyone else supporting me.
I am glad the right verdict came about in court. I am innocent, have always been innocent and have proven to be innocent.
"These legal proceedings have played an integral part of my life and also my career. I am now solely focused on working hard and getting myself where I should.
"I would like to thank Swindon Town FC for giving me a chance at a vital time to progress. I cannot thank them enough for their support."