re-routing the mic jack

is it possible to re-route the microphone jack to output sound?
My headphone jack is kinda broken.

You could just cut the wire a good length from the jack of both your headphones and microphone then switch them, but that would be a waste of a good microphone so I suggest you get a new pair of headphones instead. Unless the microphone was broken at its head and is gonna get trashed anyway. Never break working stuff for the sake of fixing something else.