I assume you mean PCI-E power connectors and not SATA. There's no SATA anything on your video card.
Either get another PSU or just some simple PCI-E power splitters. There's some that split from molex or even from a current PCI-E connector so you can attach more devices. Sure your current PSU has plenty of plain regular molex being unused.
That's good as long as you know your PSU can handle the total load. I'm powering 4 6870s on a 1000w just fine. Do 6970s require that much more power? (I don't know) but I would guess that your 1600w would be enough for it. Sure someone else would chime if I'm mistaken. *shrug*
What kind of motherboard are you using, and how many mhashes per second are you getting? atleast 400?