Firstly, IIS itself will not work on linux.
Therefore I assume you want to migrate the website, not IIS.
There are several alternative web servers for linux.
A commonly used one is called Apache. Another popular one is 'nginx'
To migrate, it will be necessary to analyse the website in terms of the languages used.
For example, let's assume it has some static HTML pages, and a CGI application in perl.
In this case, migration to Apache may be feasible, and might even be fairly easy to do.
In another case, if the website uses 'asp', it may be difficult or impossible,
because the solution on Apache may not be fully compatible with your code.