You need to deploy it in WC_Portlet managed server. (WSRP)
Register your portlet as producer in WebCenter creating a connection to your WSRP portlet in WebCenter Portal / Spaces application.
Add this portlet to Resource Catalog and add it to a page with Oracle Composer to consume it.
You have the weblogic domain right ? Opent the enterprise manager in browser by hitting the below url -
http://<Admin Server address>:<port>/em
login with credentials.
From deployments end,you can install the war file which will targeted to WC_Portlet server.
After that register the portlet WSRP url with your application and use it.
The above suggest is without the intervention of jdeveloper /webcenter.
Is your JSR 168 portlet WSRP 1.0 or 2.0 enabled? WebCenter can only integrate WSRP enabled portlets. You cannot deploy your war file to the portal itself. You need to deploy the war file to the portlet container and register the producer as a WSRP producer in webcenter. Therefore, the portlet needs to have the valid web service endpoint to act as a WSRP endpoint.