Yes you can, but be careful.

Depending how you hydrant is mounted {in the ground, in a curb, etc} you must keep the pipe from turning or you may snap the line which feeds the bottom of the hydrant. If you snap it in the curb, you can fix it, underground it will take a backhoe to fix it.

Use pipe wrenches and make sure only the head turns. You can loosen it and remove it, put new pipe tape on the threads and then tighten it down and stop at the spot you want the outlet facing.