sure, it would be great to connect an SSD to a SATA port on the mainboard...
but there needs to be a place to mount it inside the desktop.
is there such a thing as a card (either pci or pcie) that i can put a HDD on and run SATA & power cables to?
No there is no such thing as what you are looking for what you could do is go on ebay buy an old cheap PCI card that is big enough to mount it on. drill a few holes in it and mount the drive on it. Make sure you put masking tape on the PCI connector on the card itself so its not actually getting power.