The Optiplex GX620 DT uses a BTX form factor (BTX case / BTX motherboard) instead of the more typical ATX form factor.
You would need to find a BTX tower case (probably from Dell) to be able to make the switch. GX620 MT (mini tower) would be an OK choice. Looking on Ebay or other auction sites might be your best source.
You would likely need a power supply for that BTX tower which is probably a good thing since the GX620 DT stock 280W PSU makes using most recent mid or high end full size video cards impossible.