The short answer is, "No".
Ultra ATA, ATAPI, etc. are parallel interfaces. SATA is a serial interface. It might be possible for you to buy a SATA-PCI board and plug it into the motherboard, then connect the SATA HDD to that. You don't indicate what scope you have, or what OS it's running, so there may be other technical issues that will keep this from working.
Ultra ATA, ATAPI, etc. are parallel interfaces. SATA is a serial interface. It might be possible for you to buy a SATA-PCI board and plug it into the motherboard, then connect the SATA HDD to that. You don't indicate what scope you have, or what OS it's running, so there may be other technical issues that will keep this from working.