"it doesn't faze me" = 612,000 hits
"it doesn't phase me" = 1,740,000 hits
Some of the latter are, no doubt, people explaining how to use the word "faze." But one appears to be a bona fide error by an AP writer that got past an AP editor then past a Charleston Daily mail editor.
Either way, I'm shocked that the "phase" version occurs almost three times as often as the one with "faze."