As per your comment I understand that you created a web application with a Jetty embedded server.
I think the best solution for you in this case is to get a virtual machine host, install JRE, upload your *.jar
and run it from there. Given firewall permissions and correct configuration you should be able to receive requests on the 80
port. Cons? It costs. A lot.
Most of the Java hosts have already a servlet container running (almost always Tomcat) and you can only deploy your web application in it. Having an embedded Jetty server messes up everything for you.
I strongly suggest you to detach your web application (or as you called it REST server) from Jetty and deploy the *.war
in any of the multiple free Java hosts to test it online.
EDIT
Thanks to you I made a deeper research on the topic and found an interesting guide to deploy a web application with embedded Jetty server in Heroku. I've never tried it nor I know if its free, but maybe you can give a try.