Does Trunks have god ki already?
Recall how Goku had his Super Saiyan God. Although Trunks is Kaioshin Appr. It does not satisfy your question if he has god ki or not. 

Having a blue aura before the normal super saiyan aura doesn't mean he got the aura of a god. 

To make things simple since I'm watching Dragon Ball Super. Goku needs a combination of 5 people who have the blood of Super Saiyan before he had it so I think Trunks also need that too in order to achieve it.