User Experience as a discipline is not yet well-established in many universities. There are, however, degrees in related fields that you can study at a tertiary level. These include: Interaction Design, HCI, Information Architecture, Digital Design, and others.
For more information on the pros and cons of university degrees (especially when it comes to landing a job in UX) read the chapter “Step 1: Get Educated” in our eBook, Get Started in UX.
The List of UX Degrees