Can I input the JSON raw data on the Raw tab instead of adding each key-value pair under Parameters?

From the SoapUI tab you can move the cursor to your Navigation window. Select the request. Your request editor window should appear on the right side. It has four tabs: request, raw, outline, and form. For request look at the "Media Type" in the window underneath. Choose "applicaiton/json" from the pull down menu.  In the space below you can type in your json

Disclaimer: I use Groovy script for this. In my case when I run my groovy, it leaves the json in the body of the request,. In my application I don't want that after I finish the request/response. So I delete the json content in an "aftertestcase" event handler. It seems once you got your json in the window below "Media Type" it will be there for future test runs.

It's just as Bill said.