hı ı want to power up my esp32 cam with battery what should ı buy or can ı get power with my arduino nano
Definitely NOT the NANO or any other board. Buy either a battery or power bank that has voltage higher than what you need which you can step down with a buck converter and enough capacity (amps) to last as log as you need.
@sonofcy already gave you a better answer, but I've been using a 4x AA rechargeable NiMH battery pack (4.8V) in a project where CAM is awaken by a PIR sensor and save pictures in a SD card. It works for 4 or 5 days.
4.8V is connected on CAM 5V pin.
If that works, keep doing it.