Is there any way I can light up a candle with an Arduino?
A simple solution is too use nichrome wire which when a current is passes through it will heat up. You could wrap some of this wire around the wick on the candle and then power it either straight from your arduino or you could include a capacitor.
This is much safer than some of the other methods which use potentially dangerous high voltages.

I tested the nichrome wire approach and it works! See following video clip. 2 Ohm resistance and 19V for 1 second.  https://1drv.ms/v/s!AvcBubMtAczvifYZwoESAhUodOoqRA