It's a relatively short word, and acronyms are typically used for longer phrases or names to make them easier to say or write.
However, if you're looking for a playful way to abbreviate "awesome," you could use something like:
* A.W.E.S.O.M.E. (which is technically not an acronym, but rather an initialism)
* A.W.E. (which stands for "Amazing Wonderful Experience")
Ultimately, it's up to you to decide how you want to abbreviate the word!