In high school I am taking German as my foreign language, but in my free time I am self teaching myself Korean for a year through the internet and various textbooks. Korean is not taught as a class in my school, and there are no outside of school courses I can take for it. Is there a way I can make a self taught language an extra curricular? Is there a way I can prove my fluency? I have thought about taking the Korean SAT Subject test, but is that a big risk?
i’m not sure if this is what you were asking; but, to my knowledge, there is no self-taught course that will earn you high school credit. taking korean sat’s won’t help – studying for them will. why don’t you check out the korean movies and soap operas on netflix? i hear that helps a lot.
yes, a Korean high score would show your ability, but since it’s often taken by heritage speakers the odds are very high you wouldn’t score high enough. 
It can be an EC if you do more than teaching yourself the language -have penpals/FB friends, created a group, fundraised for something, went there, watch videos, maintain a website…