Yes, you can give SAT exam in class 12th but if you want to take admission, there will be a gap of 1 year because if you give SAT in 2022, then you are eligible to take admission in 2023 session.
Ideally, you should have given SAT exam in class 11th (which most of the students do) so that you can take admission immediately after your class 12th.
Regards.