Yes. Apple Music does offer an Annual plan, but they have this option hidden inside the app itself.

Here is a step by step on how to change your Apple Music plan on your iPhone, iPad or iPod Touch:

  1. Open the Settings app. 
  2. Tap your name, then tap Subscriptions.
  3. Tap the subscription that you want to change.
  4. Choose a different subscription option. If you choose a subscription that you can share with family members, make sure that you have set up Family Sharing or joined an existing family group.

Apple would obviously rather customers subscribe to their monthly plan as it becomes more predictable to predict revenues in the future on a monthly basis compared to a yearly basis.

Here is a full step by step guide on how to change to an annual plan on any device.