I have recently taken apart some old PCs and found an HDD that uses this cable, but my motherboard doesn't seem to have a connector. Is there a way to connect this to SATA or PCIE?
edit: hdd, not ssd
That is an IDE cable, the standard for consumer-grade drives before SATA came along.
Sometimes you can find such cables with three connectors, one at one end, two at the other. And sometimes, a few wires are flipped over between those two connectors.
One IDE cable could host two harddisks, and most IDE harddisks had jumpers to set them to be drive 0 or 1. With a straight cable, you had to jumper them properly, with the partially twisted cable, you set both identical, I.e. you left them both as device 0.