http://www.gigabyte.com/fileupload/product/2/4643/8233_big.jpg
If you look on the top left corner of the picture, you will see a tiny, silk screened "Rev:1.2"
That is the only model of your motherboard that actually lists support for the 8320 CPU, but at that, it only lists support for the 8320-E which happens to be a special, lower-power version. All models seem to have had updated CPU support as a function of their BIOS updates. You will want to look carefully at your motherboard, in the same location as on the picture I provided a link to, and determine which revision you have. Next you will want to select the proper revision on the Gigabyte website here:
http://www.gigabyte.com/products/product-page.aspx?pid=4643#ov
The versions are shown as small links, to the right of the make / model of motherboard.
Click Support & Downloads, then from the download type choose BIOS.
Even if your motherboard doesn't officially support your CPU, you may be able to use it just fine, but you run the risk of damaging the power feed if you run the system at 100% load for an extended period of time. What I noticed while looking through the CPU support list for that board is that the supported CPUs only go up to 95 watts. Your 8320, unless it is an -E model, is a 125 watt model.
After choosing the BIOS download location, you should have a self-extracting file that will contain the new BIOS. The recommended method would be to have a FAT-32 formatted USB memory stick attached to the computer, copy the contents of the downloaded file to the memory stick after you have run it and they have been extracted, and then reboot.
During the boot process, enter BIOS and run Gigabytes Q-Flash utility. Provided your BIOS correctly identifies the USB memory stick, you should be able to load and flash the new BIOS contained on the memory stick.