Darren Clark was named an Officer of the Most Excellent Order of the British Empire, and Rory McIlroy a Member of the Most Excellent Order of the British Empire in the New Year’s Honours List. Neither permits the golfers to use the honorific “Sir,” but they do get to add it as a post-nomial (i.e., Darren Clarke, OBE)
The Order was initiated by George V in 1917 to honor people who had distinguished themselves in non-combatant roles during the Great War. It later was split into military and civil divisions.
US citizens can become honorary members—and several have—but full membership would require renouncing US citizenship.