Yes, you can acquire magical barding
Barding is armour, and nothing in the rules prevents you from enchanting that armour just as you would any other similar item. The rules for magical armour specifically note that:
Armor for Unusual Creatures
The cost of armor for nonhumanoid creatures, as well as for creatures who are neither Small nor Medium, varies. The cost of the masterwork quality and any magical enhancement remains the same.
Which makes it clear that it is not just ordinary humanoid armour for small/medium creatures that can be enchanted, and doing so costs no more than enchanting "normal" armour (even if the base price of the armour is higher). Barding is the only other kind of armour described in the rules.
Such equipment is especially important to druids and rangers specifically; getting magical equipment for their animal companions is necessary to keep them relevant as their master gains levels, and the game (and community) generally assumes that these characters are investing appropriately in equipment for their companions.