Q:

Can I control a load of 12v DC with a solid state relay 24-380VAC? 

I need to control a load of 12v DC and 30A, Can I control the load with an  AC solid-state-relay 24-380v and 40A?  If it isn't possible, what should I use? 
Thanks.  

A:

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. 

A:

what should I use? 

You can control a 30A DC load of any reasonable voltage with a suitable MOSFET.  Your options are wider if the gate control voltage is 10 volts or above.  For switching 12 volts, I'd look at 20 volt rated devices with an on-resistance in the milli ohm range.  For a 10 milli ohm on-resistance at 30 A, the power dissipation is going to be 9 watts so, some form of heatsinking will be required. 
You can get a few MOSFETs that are around 1 milli ohm of course.  
To make this work with reliability you need to have an under-voltage lock-out system should the 12 volts drop to below 10 volts.  This prevents the MOSFET being turned on when it can only achieve an on-resistance of maybe 100 milli ohm to avoid burn-out. 
If you are switching an inductive load you will need to use a flyback catch diode rated potentially at full load current.