Yes, a website can be submitted as a specimen of use when applying for a US trademark.
Some conditions must be met for the specimen to be valid. It must show the goods or services in question. Furthermore, it must show that a given trademark is prominently used, mainly in connection to the goods and services you wish to include in your application. Lastly, the website must prove that the goods and services in question can be acquired by US customers. If your company isn't based in the US, it is sufficient to show that you provide shipping to the US.
It is a common practice to provide multiple screenshots of your website, to meet all the requirements.