That's not how it's done (because 25-pin SCSI is rather bad). You need a well supported PCI SCSI adapter, like LSI's 20860, a 50-pin cable to go with that (HD plug for the card, old fashioned Centronics style for the scanner end), and a 25-pin active terminator to go onto the other connector on the scanner.
If you want to go the cheap route, get a Tekram 305U SCSI card (it's advertized as Mac-only, but nevermind). That one has external 25-pin. You'll then reuse the original cable, but you'll still need a terminator, a 50-pin Centronics this time. But that'll screw up signal integrity badly enough that you won't be able to have anything else on the same SCSI chain.
As I said already, getting those old scanners connected to newer systems might prove expensive. And then there's the software support issue - the 1220S will run well in Linux, but is completely unsupported in recent Windows flavors.