If you haven't already done so, push your nextjs app to a git repository like GitHub, GitLab, Bitbucket, etc. It can be private or public. This will make it easier to deploy your site on vercel or other platforms.
Then follow the steps below to deploy your site on Vercel.
After signing up, you’ll be directed to the "Import Project" page. Under "From Git Repository", select your Git provider and set up the integration (Instructions: GitHub / GitLab / BitBucket).
Once the integration is established, click on "Import Project From …" to import your Next.js application. Vercel will automatically detect that your app is using Next.js and configure the build settings for you, so no changes are necessary.
After the import process, Vercel will deploy your Next.js app and provide you with a deployment URL.
FYI:You can even deploy your site on Vercel through cli by running vercel command in your terminal after installing vercel cli by running npm install -g vercel or yarn global add vercel. For more information, check out the Vercel CLI Documentation.