Yes, that's definitely a BIOS setting on most computers with ATX or newer power supplies. It's usually labeled very clearly, so if you don't see it in your BIOS, then either you haven't looked at the right page of settings, or for some reason your motherboard manufacturer didn't include it.

Make sure you're running the latest version of the BIOS for that motherboard, then look around more closely for the setting. It would probably be under "chipset" or "power" or "advanced" or some such. It would be named something like poweron after powerfail, or AC power on behavior, or some such. It would have three settings: Stay off, Power on, or "Last" (meaning it should return to whatever it was when it lost power).