Can someone who arrived to the US in their junior year go to college?

Welcome to America!

Yes definitely! According to FAFSA, you are eligible for federal financial aid under the status of an asylee just like any other citizen/PR. That I am sure of. However, I doubt you’d be considered as a domestic applicant to colleges themselves, which would hurt your chances of admission quite a bit. What are you planning on majoring in? Have you taken the SAT/ACT yet?