Depends on how you define "magic". One very clear instance, I think, was at the assault on Minas Tirith:
Then the Black Captain [i.e. the Witch-king] rose in his stirrups and cried aloud in a dreadful voice, speaking in some forgotten tongue words of power and terror to rend both heart and stone.
Thrice he cried. Thrice the great ram [Grond] boomed. And suddenly upon the last stroke the Gate of Gondor broke. As if stricken by some blasting spell it burst asunder ...
(The Return of the King, Chapter IV, "The Siege of Gondor", p. 810 in my Houghton Mifflin one-volume edition. Emphasis added.)
Why he was called "the Witch-king" may have had more to do with older meanings of the word "witch", and its roots, which come from unclear sources (although Tolkien, who worked on the etymologies of words beginning with "W" for the OED, may have had his own ideas). See here for a good discussion.