A system and method for packaging oriented containers in a container carrier wherein a plurality of containers are fed into an orientation wheel including one or more chucks. Each chuck engages one end of the container and rotates the container into an oriented position. A transfer belt having a plurality of tactile fingers is operatively connected to the orientation wheel and transfers an oriented container nested within the tactile fingers in a fixed rotational position from the orientation wheel to a packaging machine. In a method of packaging containers according to this invention, multiple containers are positioned within the carrier in one or more rotational positions based upon the desired appearance of the package.