It is possible, but you need to talk to Corps Staff to get the okay. Have you done a Spend the Night with the outfit you want to join? That is a good way to really check out if they would be a good fit for you. My son is in an Army outfit, and one of the leaders in his outfit switched over to Air Force, so it wouldn't be the first time one branch was mixed into another branch.
And congratulations on getting into A&M Engineering! You're obviously a very motivated person to be majoring in one of the most demanding courses of study at A&M and to take on the responsibilities of being a cadet in the Corps as well. Gig 'em!