I'd like to know if playing an Aarakocra character is currently legal in the D&D 5e Adventurers League.

The Aarakocra race has been in D&D for a while, but is described in detail in 5e in the Elemental Evil Player's Companion on page 3.

"This chapter presents three new races to supplement thos in the Player's Handbook... These new options are available when you make a character, provided that your DM allows them in your campaign"