Litmus as a substance is used to differentiate between acidic and base solutions. This substance exists in 2 colors, red and blue. Also, it exists in two forms, paper, and solution. When in basic solution, the blue litmus will remain unchanged, however, when in acidic solution, it changes to red.
Ferric chloride on the other hand is an acidic solution, which is formed as a result of the interaction between a weak base (iron oxide) and concentrated or strong acid (hydrochloric acid).  Therefore, since ferric chloride is acidic, the color of the blue litmus will change to red when it is introduced into a ferric chloride solution.