Can I have my rotors cut on my 2009 Dodge Charger or must I replace them?

You need a set of calipers, the measuring type, to measure and what the minimum thickness recommended. These days rotors are really inexpensive for most models, it's almost not worth having them cut

Or micrometer to measure

Yes your rotors can be turned unless they are slotted and drilled ...but being that its an SXT model I'm sure they are just standard brakes ...they should be measured for thickness and out of round to make sure they can be machined....the rotors slip on over the hub ...they my get stuck to the hub due to rust but a good size heavy soft face dead blow hammer will knock them off if you gonna do it yourself ...also now a days it may cost you the same amount to just replace them them to waste the time to machine them ..also if they are heavily rusted its just better to start with new ones