The Answer:

According to the U.S. Mint, The likeness of President Abraham Lincoln on the penny is an adaption of a plaque executed by portraitist and sculptor Victor David Brenner. President Theodore Roosevelt was so impressed with Mr. Brenner's design of a Lincoln plaque that he recommended to the Secretary of the Treasury that the design be placed on a coin to be issued in the Lincoln Centennial Year, 1909.

The direction that Lincoln faces on the cent was not mandated—this was simply the choice of the designer.

—The Editors