From your question I'm assuming, you want to directly run your WSGI-compliant app with uWSGI and open an HTTP-Socket. You can do so by configuring your uwsgi.ini (or whatever the filename is) with
http=127.0.0.1:8080
uwsgi will now open an HTTP-socket that listen on port 8080 for incoming connections from localhost (see documentation: http://uwsgi-docs.readthedocs.org/en/latest/HTTP.html)
Alternatively you can directly start your process from the command-line with the http-parameter:
$ uwsgi --http=127.0.0.1:8080 --module=yourapp:wsgi_entry_point
If you use unix-sockets to configure uwsgi nginx is able to communicate with that socket via the uwsgi-protocol (http://uwsgi-docs.readthedocs.org/en/latest/Protocol.html).
Keep in mind, that if you usually serve static content (css, javascript, images) through nginx you will need to set that up, too, if you run uwsgi directly. But if you only want to test a REST-API this should work out for you.