The 'RIP' singer - who performed at Glastonbury at the weekend - posed topless for the men's mag, as she told them she is "falling in love" with Calvin.
“It’s early. I’m not in love. But I’m definitely falling," she said.
The couple went public with their romance in May, after first being linked when they were seen leaving LA's Chateau Marmont together a month earlier.
The pair have spent a lot of time together in LA, and Rita also told GQ of how she misses her family and friends when she is away from home touring.
“You always have to sacrifice something when you want to achieve something. Of course, I get lonely and I get sad, but I made a decision to do this... I’m in an amazing position to change my life, and change my family’s life," she said.
On her meteoric rise to fame, she added: “We control what we let out in the media. Social media is so influential now. I feel like I’m lucky to be in this position now, in this time. Because there’s nobody else to blame if it all goes tits up.”
The full interview appears in this month's GQ magazine, on sale from Thursday 4 July.