Hi, Kristina!
Welcome to the Disney Parks Moms Panel, and thanks for your question. As a Starbucks lover myself, I was thrilled when plans were announced to bring some of my favorite Starbucks food and beverages to theme parks at Disneyland Resort and Walt Disney World Resort.
The Market House, which will serve Starbucks, is scheduled to reopen on Main Street, U.S.A. next month at Disneyland Park. At Disney California Adventure Park, where Starbucks has been open since last summer inside Fiddler, Fifer and Practical Café on Buena Vista Street, Starbucks Cards are indeed accepted. I have even been able to use my Starbucks Gold Card there, and I suspect the same will hold true for the Market House location when it is open.
I hope this helps, Kristina, and that you have a wonderfully pixie-dusted visit to the Disneyland Resort! Please write back with any other questions you may have.
Wishing you magic,
Courtney