Yes, absolutely you could learn cybersecurity on your own. You don’t need to pursue a degree in cybersecurity specifically to get to know about the domain. For self-learning, you could just enroll yourself in a good course and get practical exposure by doing guided projects.
For this, I would recommend you to take up the Cyber Security Course from Intellipaat which offers you a training course of 30hrs that is available as instructor-led and also as self-paced videos along with 60hrs for gaining hands-on experience through projects and exercises.
I would suggest you watch our YouTube video on Cyber Security Tutorial.