There's two steps. Adding the partner card to the app so you can use it in stores, and linking your partner number to the mobile app.

https://www.starbucks.com/account/signin

Go to the account page. You might need to turn on desktop mode if you are using a phone. At the bottom of the "Personal Info" link, click on "Add your partner number." and follow the instructions. NOTE: It might take a day or two to update in the app.

It works when I mobile order, I believe you can do the thing where you add a starbucks card but just put the card number as your partner numbers. Or you can do it on the web instead of the app which is probably more reliable, I’d try both and then see if it’s still not working :)