Yes there are inexpensive and easy to use adapters connecting a newer SATA HDD to an IDE (PATA) connector or cable.
The older computers usually have 2 IDE connectors. If one IDE connector is free, there are small adapters that fit right onto the IDE connector on the MB, with usually a couple SATA connector ports going out to SATA drives. They take up the whole IDE MB connector. You can also get a similar adapter that connects a SATA port to the drive, with the IDE cable connector being plugged into this adapter. Most of the adapters require a smaller "Berg" power connector to power the adapter chip or a regular Molex connector to power the adapter chip and HDD together.
Here's an image where the IDE cable plugs into the back of the connector along with a molex power connector, and the bottom image shows the data and power sata connectors into the SATA drive.
Both are available on Amazon or NewEgg for less than $15, but you have to be careful to choose the specific one you want, that connects an IDE type MB or cable to a SATA drive.
They also have ones that connect an older PATA CD or Drive to a newer SATA MB cable which you wouldn't want in this case.