Not sure how you would do that, considering the PS2 controller has no wireless/bluetooth capability nor a battery to power such a thing.
Yeah, I was wondering that too. PS2 was corded or whatever the third party used. There were no first party cordless/wireless controllers.
Get an 8BitDo controller that has native BT support. They are amazingly well built and not very expensive. It's $30.
8Bitdo Ultimate C 2.4g Wireless Controller: https://www.amazon.com/dp/B0C2V3QPN7
It has a dongle, too, for faster connectivity to PC or anything with a USB port.
It even has Android software for remapping controls, and macros, etc.
I used to be able to connect a dualshock to my Note 3, and I remember it being pretty bang simple. PS2 Dualshocks use Bluetooth. But maybe the modern Bluetooth protocol is incompatible, I haven't tried with my newer phones.
Edit: Ah wait, I'm remembering wrong. I used a dualshock 3, like for the PS3. Those ones use Bluetooth. Not sure about the wireless dualshock 2s. They might use some proprietary 2.4GHz connection.