That file size will cause a LOT of problems with protocols expecting a 4-byte (aka, 32 bit) file length (2.14 GB limit). I suggest 3 things:
1. SCP *should* work, I've done big files with it. Posting the specific error message might help us get it going.
2. Rsync will also handle big files, preferrably with rsync over ssh (rsync -e ssh).
3. You could use "split" to split it into a number of <2GB files, transfer them, and then recombine it on the other end. I'd be happy to help you with any of these, just ask.