It's not an indigenous species and therefore shouldn't be covered by ANY of our game laws. Same as a wild hog as far as I'm concerned.
Unfortunately this isn't the case. The American alligator is considered to be a native species in the state. Surely being from Cartwright you heard about the gator that was caught around Tishomingo and released back into Lake Texoma by the local game wardens.
http://www.kten.com/story/11502637/alligator-caught-released-in-johnston-county