It should, as long as the motherboard has a PCI-E x16 slot and the power supply cables to supply the GPU unless the GPU can get power from motherboard directly (only if the GPU has no power pins on it). Then you should be good. Looks like the GT 610 doesn't have power pins, you should be good to go as long as there's a PCI-E x16 slot 2.0 or higher. You should have at least a 300 watt power supply.
Edit: Your PC has a PCI-E x16 1.0 slot, but it can still work.