When I bought couple of domains and was looking to find a way to host more websites on a single server. Aperantly Godaddy does not allow to put a Server IP address with a specific port on it. The option is to just leave the A record as @ and the Value to be "Parked" which means it is not pointed to a specific IP address. Then navigate down to the DNS page and find a section that says "Forward", select (http:// ) then type the IP address of the Server with the Port number where you are hosting your web application e.g 123.678.5.3:PortNumber.
Make sure you fill in all the blanks about the website and select "Forward with Masking": What forward with masking does is, it hides the servers IP address and shows whatever Title you write in the Title section. So, when I forward domain name hosted on www.domainName.com hosted on 123.678.5.3:PortNumber and the Title of "MyWebSite", whenever the user goes to www.domainName.com it shows "MyWebsite" in the URL section.