This is an entry in our Disneyland 101 Glossary: Disneyland Resort definitions in under 101 words, from Mouse Brief.
At the time of this writing, it is possible to schedule a character wake-up call at Disneyland Resort Hotels. Guests can use the room phone to call guest services at the hotel and let the cast members know what time they would like to be woken with a phone call on the room phone. The cast member can share which characters and what kinds of greeting are available before they schedule a call for the requested time.