My first singleplayer world and I found the unicorn and the titanosaur right next to each other at the edge of the Red Woods. The way I tamed mine was I put it in a wooden box with window walls and I went prone under the window and the next time the unicorn poked his head out, I was able to feed it without spooking. Having the Ghille Suit makes it much easier too.

More Unicorn Taming & KO Tips