Gayathri Ajith said he sent the inappropriate Whatsapp messages to her in December 2015, three months after they met on a flight from Manchester to Dubai.
Ms Ajith, who was 16-years-old when they met, said she told the professional cricketer she was 17 to “seem a bit older” and agreed to have a vodka coke with him on the plane, but turned down an invitation to have dinner with him in Dubai.
Screenshots of messages from a number belonging to Mr Rafiq, sent in December 2015, read: "u know what I wanted to do on the plane?" and "I want to grab you push u up against wall and kiss you".
When she said "do you realise that I'm only 17?" she was asked: "Does tht mean it not allowed to want to kiss me" and “Wud u have let me kiss u?”.
Ms Ajith, who is now 22 and lives in Yorkshire, described his message as "creepy" and was so perturbed by Mr Rafiq, she asked: "How do I know that you're no some absolute pervert"?.
She told The Yorkshire Post: “I was just kind of shocked by the crudity of those messages. They were just so vulgar.
“I'm not disputing any of his racism claims, because I'm sure they're very true experiences. But certain aspects of what he said just don't really sit right with me.
“If he was being forced to drink by his teammates, then surely that wouldn’t then mean he would be drinking alone on a flight and encouraging a 17-year-old girl to be drinking with him."
She added: “His behaviour towards me was a direct contradiction really of what he said in his testimony.
“He's calling for equality and respect, but why is he not embodying that in all aspects? Especially in his tone towards women. It’s hypocrisy.
“He is being put on this pedestal for inciting systemic change, but he's really contributing to the problem of the vulgar attitudes towards women. The whole nature of that dosen’t sit right with me.”
A spokesman for Mr Rafiq said: “This was put to us late on a Friday evening. We need to look into this, so cannot comment further for now.”
Mr Rafiq has been praised for calling out the racist abuse he suffered at the hands of coaches and teammates while playing for Yorkshire County Cricket.
It comes after the club conducted an investigation which found that the former spin bowler had suffered racial harassment and bullying, but decided that no-one would face disciplinary action.
The married 30-year-old, also told a Digital, Culture, Media and Sport select committee this week that English cricket is "institutionally" racist, but by speaking out he hopes there will be "massive change in five years' time".
Earlier this week, he apologised after it was revealed he had posted anti-Semitic messages as a teenager in 2011.