Okay Claire... I've added a "beginner" prefix to this thread - hopefully it'll prevent too many "smart arse" replies.
You've asked a bit of a loaded question I'm afraid... The thing is, for portraits, the camera doesn't matter to the same extent that the lighting, the lens, the posing and the interaction with the photographer does. Yes - it CAN have an effect, but to be honest, any half-decent SLR or mid-range mirrorless camera body will be fine.
Looking at (for example) one of the most prestigious UK portrait competitions, the Taylor Wessing Portrait Prize, the 2015 was shot on a Sinar P 10x8 film camera, the 2014 winner was shot on a lumix GF1 compact systems camera, the 2013 was shot on a 4x5" Film Camera... both of these are FAR from the kit that typically would be used by typical working pro's - who'd generally be using a Full-Frame Digital SLR - something of the ilk of a Canon 5Diii / 5Ds / Nikon D810 or similar from the Nikon Product range...
Maybe you can add a little more information - are you asking for a recommendation as to what you should be looking for in a camera you wish to buy, or, are you simply asking what would be peoples "dream camera" for shooting portraits... Either way, I'm afraid you're going to get lots of conflicting suggestions on the hardware, as people have their own preferences - but I'd hope that one thing that will go across the board is that most people on TP will be clear that ultimately the defining thing in terms of quality for portraits is unlikely to be encapsulated in a single model of camera body...