Hi!

DNS only handles domain -> IP mapping. It cannot map the default port (80) to a custom port–you will have to use a reverse proxy for that. nginx is one of the most popular reverse proxies that are used to do that.

First, add a DNS record for your subdomain.

Then, install nginx:

• How To Install Nginx on Ubuntu 14.04 LTS

Add a new server block:

server {
    listen 80;
    server_name myapp.domain.com;

    location / {
        proxy_pass http://localhost:8080;
        proxy_set_header Host $host;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto $scheme;
    }
}

Finally, enable it and restart nginx:

sudo ln -s /etc/nginx/sites-available/myapp /etc/nginx/sites-enabled/myapp
sudo service nginx configtest
sudo service nginx restart

You should now be able to browse to http://myapp.domain.com and see the contents of http://your droplet's ip:8080.