Is there any way to use an ac load ssr with a dc load
You need to choose something suitable for DC.

Your relay has a Triac output. The problem is that in order for a Triac to turn off, the current must drop to near zero. For AC, that would happen every half-cycle; but for DC that would likely require turning off the DC supply.

12V @ 0.5A is a pretty simple requirement. For a low-side switch, an N-channel MOSFET would work nicely, although if your load is inductive, you will also need a flyback diode.