Your ARN is a 7-, 8-, or 9-digit number. You should be able to find it in any of these places:
On the top right corner of your Immigrant Fee handout.
On your visa stamp (also known as a visa foil) in your passport. Your A-number will be called the “Registration Number” on the visa stamp. If the number is fewer than 9 digits, put a 0 after the “A” but before the numbers.
Example: A12345678 becomes A012345678
On the front side of your Permanent Resident Card (AKA your Alien Registration Card or Green Card). It may be listed as an "USCIS#" depending on the year it was issued. Here are two examples:
On any letter or notice you have received from the Department of Homeland Security.
Unfortunately, there isn't an online portal where you can look up your Alien Registration number.