No, you do not need a specific degree to be a UX Designer, but you do need the right hard and soft skills to be considered for a role in UX design. In fact, there’s no such thing as a Bachelor’s of UX Design—everyone working in UX design today began in an affiliated field like product design, graphic design, or web development, or by gaining related experience, before picking up the additional skills they needed to call themselves a UX Designer.
Some of the most successful Designers have no formal training in UX. Facebook’s VP of Product Design, Julie Zhuo, joined the company as a Software Engineer. President Emeritus of AIGA Debbie Millman was an English literature major. And you wouldn’t think electrical engineering or mathematical psychology relate to UX, but Don Norman is widely regarded for his expertise in design and usability.
Essentially, what a Hiring Manager’s criteria come down to is this: does a candidate have the requisite skills—and can they prove it?