How do you normally establish trust? Is it from discussions? From shared experiences? To find the closest possible thing we need to know what the in-person thing would be.
A few options would be, if you like the physical aspects of things, to exchange letters and every so often physical items. The shipping will add up, though.
If you like shared experiences, then you could possibly watch a movie together over the computer, or play a game... but I'm not sure if you'd want to do either. You could also read a book at the same time and talk about your impressions for instance.
If it's discussions, then the solution would be to talk often, obviously.
If you normally get close through experiences and physical things, it's going to be the hardest. If you get close through talks, even if they have to include voice, it's already much easier to keep that aspect in a LDR.
How often do you see him while he's away? How much do you know about his life when you're not talking?