Can I control a load of 12v DC with a solid state relay 24-380VAC?
No you can't.



Figure 1. The SSR-40 DA.


  I need to control a load of 12v DC and 30A ...


The device clearly shows that:


The output (pins 1 and 2) are AC. It can not switch DC.
The output will switch 24 V to 380 V AC. Even if it could handle DC your voltage is too low.



  If it isn't possible, what should I use?


A relay or a DC SSR with voltage and current ratings to suit.