Generally, no...
##Generally, no... TheThe Adventurers League Players Pack contains the documents that detail your options in AL play. Purchases are restricted to items in the PHB. The only potion available for sale without special documentation is the basic Potion of Healing. There are no other magic items in the PHB - no potions, no scrolls - so they can't be purchased either.
...unless you're of sufficient rank in a faction...
##...unless you're of sufficient rank in a faction... CharactersCharacters who reach rank 3 in their faction can use downtime and gold to acquire magic items from a very limited list: +1 weapons, shields, and armor are available to all faction members, and each faction allows access to a single uncommon item and a single rare item.
...attend an event featuring Fai Chen's Fantastic Faire...
##...attend an event featuring Fai Chen's Fantastic Faire... Fai Chen's is available to public events of sufficient size that register with WoTC for it in advance. Fai Chen trades (but does not sell) permanent magic items, sells scrolls up to 5th level (one per transaction per event), strange trinkets, and occasionally special mounts and property deeds.
...or adventure in Chult.
##...or adventure in Chult. ThereThere is a very small number of magical weapons and shields, plus scrolls and potions, available for purchase only to characters playing Season 7 content - DDAL modules and Tomb of Annihilation. These purchases are only available as a downtime activity.