Vercel is a serverless platform with support for 35+ frontend frameworks and does not support running docker instances.
While you can't deploy Docker images to Vercel directly, you can use Docker as part of your local development workflow when building for Vercel.
Running Docker Locally
Docker can be useful to ensure your website works on the same on any machine. By creating a Docker container, you can explicitly define the required dependencies to build and run your application on your local machine.
Since Vercel has zero-configuration support for many frontend frameworks, you might not need to use Docker to deploy your application. However, Docker can be used for reproducing the same local environment across machines. For example, here is a Dockerfile used with Next.js.
To verify and run Vercel builds on your local machine, you can use vercel build to run your application's build without pushing your code to Vercel.
Further, if you don't want to send your application source code to Vercel, you can use vercel deploy --prebuilt to upload the generated build output from vercel build (located in the .vercel/output folder).