Yes. Test administrators will provide you with 2 pieces of scratch paper, 2 pencils, a sharpener, and an eraser right before you walk into the test room. The scratch paper provided should be enough for most people, but if you need more, you can raise your hand, and the test administrator will give you more.
Any belongings such as smartphones, books, laptops, etc. will need to be stored inside a locker. One of the test administrators will give you a key to a locker when you check-in at the front desk.
You can use the scratch paper to write anything on it and use it in any way you wish; however, you cannot take the scratch paper with you during your break outside the room.
Moreover, once the test is complete, you will have to handover your scratch paper to the administrator. You cannot leave the premises with the scratch paper. In case you want to write down your unofficial GRE score displayed at the end of the test, you can ask the administrator for a post-it note or just any separate piece of paper.
Make sure you empty all your pockets before entering the test room of any pieces of paper that can land you in trouble if found.