There are two ways for players to capture their own Galarian Ponyta in Pokemon Go.
Raid Battles: Galarian Ponyta appeared in Raid Battles until October 23rd. It is likely it will return in the near future.
Eggs: Galarian Ponyta will appear Yellow 7km eggs. Use Incubators to hatch them as soon as possible.
They are also in raids right now according to Leek Duck
Here you go!
Ponyta have been in Tier 1 raids in the past multiple times for events and hatch from 7km eggs. Not found in the wild yet, though
source + experience