Technically you don't need any special server as long as your application can receive http requests and send http response ( I assume you restful service runs on http).
However most of the Java Restful services run on some kind of Java Application Server which support Java Servlet Specifications like Tomcat.
You can host it at home (if you have good internet connection and static ip), AWS or at some hosting company. Some companies provide installations or you can install one yourself on the VM provided