Yes, you do. Amazon's program policies and US laws require you to disclose that you'll earn a commission when users buy a product.
It is not just limited to Amazon. All websites that use advertising or affiliate marketing to make money need to show a disclaimer. For an example, you can see our WPBeginner's disclaimer page.
To meet Amazon's requirements, you must include a legally compliant disclosure along with your affiliate links and identify your site as an Amazon associate.
You must also include the following statement on your website:
"As an Amazon Associate, I earn from qualifying purchases."