You can change the default ports by editing the server.xml file here:
Look for a line like this and change the port value:
<Connector maxHttpHeaderSize="65535" connectionTimeout="20000" port="6080" protocol="HTTP/1.1" maxPostSize="10485760" redirectPort="6443" server=" "/>
If you have SSL enabled, find the <Connector> line with SSLEnabled="true" and change the port value. With either of these, you will then need to restart the ArcGIS Server service for the changes to kick in.
Don't do this unless you know what you are doing.
Link that identified this for me: http://gis.stackexchange.com/questions/48591/changing-arcgis-server-10-1-port-6080-to-8080
As per ESRI’s documentation it is not recommended to change default ports for:
As ESRI technical documentation does not provide any information for changing those ports. ESRI only provide documentation of using non-default ports with Web Adaptor for ArcGIS. Even in that instance, it is considered as rare cases where Web Adaptor cannot use default web ports 80 for HTTP and 443 for Secure HTTP. Otherwise, ESRI even recommends to keep the default ports for the Web Adaptor.
To protect the identity of Enterprise GIS Servers a reverse proxy is deployed within a perimeter network (also known as a demilitarized zone [DMZ] or screened subnet) that handles requests from the Internet and forwards them to the machines in your internal network. The forwarding of requests on behalf of the reverse proxy server masks the identity of the machines behind your organization's firewall, thus protecting internal machines from being attacked directly by Internet users. Additional security functions can be implemented in the reverse proxy server to further protect your internal network from outside users.
While it is possible to change the default ports that is not a configuration that ESRI would support. Changing the default ports for ArcGIS Server, Portal, and/or Datastore may impact and/or break your ArcGIS Enterprise implementation.