Yes, you can learn SEO on your own. Many SEO professionals and marketers have taught themselves by reading articles, watching tutorials, and experimenting with personal websites.
Learning SEO takes consistent effort and a willingness to learn from mistakes and successes, but the process is entirely doable. Breaking SEO into steps such as keyword research, on-page optimization, and link building allows you to build a strong foundation one step at a time. As you see small wins, you gain the confidence to keep going, knowing that many others started right where you are and achieved real results.
Further reading: How to Learn SEO