Yes. Per their website:
Order Cancellation Policy: Orders placed with Palmetto State Armory may be cancelled by the customer prior to the item having shipped. All cancellation requests must be made through the Customer Service Department, reachable by phone at (803) 788-9095, during customer service hours of 9:00 A.M - 6:00 P.M Eastern Standard Time, Monday through Friday. If the item/package has shipped, the order may not be cancelled and the customer must follow all rules applicable to returns. Please note that the return of the item/package will be made at the customer's expense. Any order that was previously cancelled by the customer may not be reversed. All cancellations are final.
I got my money back within 2-3 weeks, and that was around Christmas and New Years last year. Ordered 12/20, and canceled between Christmas and the 31st.
Just a warning...order may or may not still be processing. My canceled order from almost a year ago is still showing "Processing", as are three other orders I placed over the summer that all the parts are in my hands.
EDIT: as info, I was not charged any type of restocking fee