I'm flying from New York to Romania with Turkish Airlines. I've searched everywhere. Am I allowed to bring a video card (original box + receipt) in my carry on?
Yes. It is allowed, as are laptops and most other consumer electronic devices. You can carry an Xbox One with you without issue.
The only complication you might face is TSA, and the equivalent at IST, considering it a "large electronic device" in which case, it will have to go through the scanner separately.
The box and receipt are not part of the equation.
This of course assumes that the device fits within the airlines carry-on dimensions though I can't imagine a video card that wouldn't.