Cloud Imperium said a couple of years ago (yes, it's been that long) that Star Cititzen will require fairly hefty hardware: A dual-core CPU, 4GB of RAM, and a GTX 460 display adapter. Six months later, a follow-up forum post jacked the minimum spec up even higher, to 8GB of RAM.
"We are creating this game with the PC gamer in mind. Of course performance will be optimized much further than our current version of Arena Commander but I wouldn’t expect that we would drop the system requirements any time soon," he explained. "Additionally on the Direct X 10 front, as almost every engine/rendering we’d like to put in relies heavily on DX11 and even DX12 or Mantle I can’t see DX10 cards even existing much longer. It’s difficult to say, but I don’t expect that the majority of gamers would even have DX10 cards anymore and so for us to continue support it wouldn’t make sense."
Of course, if you're gaming on a PC with 4GB and a DirectX 10 card, the odds are that either you're playing Peggle, or you're already looking into a fairly major upgrade. And by the time Star Citizen rolls around, which isn't likely to happen for a couple more years, that sort of system will be just about completely untenable for any kind of gaming that isn't built into Windows.
An Intel Core i5 2500 and a GTX 670 GPU is recommended, while "a smooth experience at maximum settings" will demand an R9 290X or GTX 780. To play it properly in 4K, you'll need to either slap together a pair of mid-to-high end cards, or wait for Nvidia or AMD to invent something new.
For the record, the minimum system requirements as they currently stand are:
Windows 7 or 8, 64-bit only
Dual-core CPU - Intel Core2 Duo 2.4Ghz or AMD Phenom X2
Nvidia GeForce 460GTX or AMD Radeon HD5850, DirectX 11 only