FAQ:

Question: Some of the internships I am applying to ask if I am legally authorized to work in the US and I am not sure how to answer since I am an international student. How do I answer?

Answer: YES, you are authorized to work in the US with your Student Visa. (You will get CPT authorization through Soka. The employer does not have to sponsor you, or do any paperwork related to CPT). If hired, the documentation you will need is your passport and a US Social Security number.

Sometimes employers ask a different question to get at if you will need work visa sponsorship after you graduate. Those questions often look like this: "Do you require work visa sponsorship now, or anytime in the future?" . This question is hard because although you don't need sponsorship for CPT or OPT (CPT: while at SUA, OPT: one year beyond graduation), if you stay in the us beyond your Student Visa timeframe you may need work visa sponsorship. The issue is that sponsorship is VERY expensive for companies, so they often try to filter out anyone who might need sponsorship in the future. They are looking to hire and train people to work in the company long term, so don't want to invest in training someone they might need to sponsor.

How to apply for CPT at SUA - LINK