Of course! You can 100% get into marketing without a marketing degree. I'm a head of marketing at TSR and have a history degree, my exec has a journalism degree, my other exec has a marketing and events HND but I would happily have appointed her without it. My Chief Marketing Officer (boss) has a economics degree.
When I interview grads I look for a basic understanding of a few marketing principles, some digital credentials and super-hot organisational skills / indication they will work well under pressure.
Marketing principles - just using words like "tone of voice", brand / direct response, content marketing, customer acquisition / cost per acquisition, creativity etc. is enough to make me confident they "get it" enough to be able to work with them to develop their skills.
Digital credentials - I love to see a blog, employer suitable twitter account (ideally on marketing or comms), insta account with loads of followers - if I'm asking someone to position my company online I'd be reassured they can position themselves online