As a general rule, no, you cannot buy magic items. But there are a few exceptions.

Buying Spell Scrolls and Potions

Spell scrolls and potions can be purchased. Please see Consumable Prices for more information.

Buying Magic Items During Adventuring

Some adventures (usually only in specific hard covers) permit you to purchase certain magic items. Speak to your DM or read the AL Adaptation Guide (see Documents) about that.