Optiplex gx820 can i connect 300 watt power supply

If it is a Dell Optiplex power supply then yes. The Optiplex has a special power supply made specifically for Dell it has an extra 6-Pin connector that is called the Dell 6 pin connector not the same as a 6 pin PCIE connector.

GX820? Can't help you much, being that there is no GX820.

I figured they meant the GX620.

If it is the mid tower version you may have a chance that it is a standard power supply, but if it is the SFF version then it can't be done with a standard power supply. Only way to know for sure is to look.