African-American dialect has often been criticized for the use of words such as "ax" instead if "ask," but critics may want to check their Chaucer, who used "ax" in his writing. Shereen Marisol Meraji of All Things Considered has the audio story.
Jesse Sheidlower, the president of the American Dialect Society, says you can trace "ax" back to the eighth century. The pronunciation derives from the Old English verb "acsian." Chaucer used "ax." It's in the first complete English translation of the Bible (the Coverdale Bible): " 'Axe and it shall be given.'