Peel the carrots. Cut them lengthwise in 4. Then, cut them lengthwise into thin sticks. Make sure they fit into your 16 ounces (500 ml) glass jar and trim the ends if necessary.
Cut the piece of ginger into slices. No need to peel it.
Add the rice vinegar, water, salt, and sugar to a small saucepan. Bring to a boil and wait until the salt and sugar have completely dissolved.
Add the carrot sticks to a glass jar. Pour the vinegar brine on top and add your ginger. Fill up the jar with water if you don't have enough pickling liquid. Close it with a lid and let it come to room temperature.
Place it in the refrigerator overnight or for at least 20 minutes before serving.
Notes
As an alternative to matchsticks, you can cut the carrots into larger sticks or into ribbons using a vegetable peeler. Larger sticks are great if you want to eat them as a snack as they provide a better grip and ribbons are perfect for salads.
You can store the pickled carrots for 2-3 weeks in an airtight container in the refrigerator. Make sure they are constantly covered in pickling brine to prevent them from going bad.