Can I specify a TCP/IP port number for my web-server in DNS? (Other than the standard port 80)

Setup and configuration

Unfortunately the standard DNS A-record (domain name to IP address) used by web-browsers to locate web-servers does not include a port number.
Web-browsers use the URL protocol prefix (http://) to determine the port number (http = 80, https = 443, ftp = 21, etc.) unless the port number is specifically typed in the URL (for example "http://www.simpledns.com:5000" = port 5000).

If you need to run a web-server on a TCP/IP port other than 80, the visitor will need to specify this port directly in the URL (see above), or you need to point the DNS A-record to the IP address of a different web-server (running on port 80) which redirects your domain name to your own server IP address and port number.
For details, please see the reference articles below.

REFERENCES:
For more information, please see the following knowledge base articles:

KB Article Web redirection and "cloaking" with classic ASP script
KB Article HTTP Redirector Plug-In