Yes, but if you want use 'having', say 'I'm having Korean lessons this year'.
To sum up:
I'm learning Korean.
I'm taking a Korean course.
I'm having Korean lessons.
One thing that was really a turning point for me was when I learned Spanish. I was always kind of scared of learning a foreign language , yet I was really envious of kids who could speak another language. But when I started learning Spanish, I found I was actually pretty good at it, and the moment I reached that breakthrough stage – you know , when you discover you can actually speak and communicate with people in the language- I felt really proud of myself. I realized that learning a foreign language wasn’t impossible thing after all. Now I can speak three : Spanish, Italian, and German. And I’m ....... Korean this year.
a. Learning b.taking c. Having d. All are correct
please choose