I'll give it a shot, but as a disclaimer: if you're asking this, I assume you're not familiar with French pronunciation in general. That's fine, but what it means is that people won't expect you to get it exactly. A pretty close name that English speakers are familiar with is probably Soren.
If trying to pronounce Sorin exactly right as a French name, you'd say: /sɔ.ʁɛ̃/ Google Translate gives an idea of what this sounds like here. The first syllable is easy, more or less like English.
The second syllable begins with the guttural French R that starts at the back of the throat. I would avoid thinking of it as "n-h" even if it sounds like that at first. You can hear it here (click "play" on the right). If that's a little hard to learn just now, you can settle for a more Spanish "rolled" R, like the one here. It can sound a little regional, but you might still consider it a trade-up from the English R.
Then it ends in a nasalized "eh" sound. Try saying the word "wren" slowly, but then stop yourself just before you actually pronounce the "n".
It's important to note that the accent is on the second syllable.
I have a pretty weak mic, but here is a recording with four options. The first two are with French R, the next two with Spanish R, the fifth with English R, and the last just pronouncing it like an English name. (In these examples the foreign R sounds are highly emphasized to make them clearer.)