So basically, the answer is you don't. It's possible that there's some really hacky way to make this work, but the odds that you actually want to do this are exceedingly low. Instead, run Rails on a non-privileged port, and set up a real web server like nginx to forward to Rails.
As a super-simple example, with nginx you might use a config file that looks something like this:
upstream rails_server {
server localhost:3000;
}
server {
listen 80;
location / {
root /home/deploy_user/rails_app/public;
try_files $uri @missing;
}
location @missing {
proxy_pass http://rails_server;
proxy_set_header Host $http_host;
proxy_redirect off;
}
}
This solution is also better long-term, because it makes your infrastructure more flexible. For example, if you need to scale up your application to multiple machines you could use nginx as a load-balancer and have it forward requests to a whole bunch of Rails servers running on different machines.