On June 20, 2019, FAA began publishing telephone numbers that pilots can use to call ATC for IFR clearances and cancelations (see FAA Completes ATC Phone Number Plan). The numbers appear in the airport listings in the Chart Supplement.
Leidos FSS has posted ARTCC clearance/cancelation phone numbers on its website, here.
If you use ForeFlight, you can also find those ATC numbers in the airport listings. As the screen capture below shows, the information is on the Frequencies tab. The number will be either to an approach control facility or an enroute traffic control center, depending on which facility controls the airspace overlying the airport.