By default Aloy is able to carry a total of 20 arrows at any time. Crafting them is quite fast, but it is also possible to increase arrow capacity. This can be done in the same way that all other craft able and carry items can have their capacity levels increased. Take the following steps to increase arrow capacity.
Pause the game by pressing the touch pad. Press L1 to navigate over to the crafting tab. Go down the menu to the carry bags and press X. This will reveal a list of different carry pouches and bags that you can upgrade in order to increase the carry capacity. You will see the arrow capacity bag on this list. You can upgrade the capacity a total of 4 times.
I have gone into detail for Horizon Zero Dawn Inventory Carry Capacity Upgrades in the main walkthrough.