Is there a way to request ASVAB scores?

did you actually enlist? If so, it’s part of your personnel record.

If you enlisted, they are with your records like TaoSan said. In the Air Force they can be found in the Virtual MPF, not sure about other branches.

If you just took it your junior year or high school or something, I’d check with the school. The military recruiters have a list of each major high school as well, but I’m not sure how long they keep them. You’d probably have to re-take the ASVAB anyway if you are planning to enlist.