SATA spec is not capable of delivering that amount of current. If the PSU has Molex (the 4 pin connectors) then you can use a Molex-->6-pin convertor. SATA should never be used for PCIe cable - I'm surprised a company could get away with making those cables since I don't know of any low power application that uses that 6-pin interface.
Well it is very conditional. I ran BFLs and tons of GPUs off of molex--> 6 pin and never had an issue. But I always made sure the PSU was up to the task, had enough power on the 12v rail, made sure the cable was thick enough and the connectors/cabling wasn't getting too hot.
If the OP can't ensure this then he should buy a new PSU unfortunately. Server PSUs are cheap.
Honestly, if it's a cheap old supply you'd be better off cutting the end off the 4pin CPU cable and just wiring the two yellow and two black wires into the screw terminals than using a molex to PCI adapter.