I'm trying to apply WPS for local shapefile. Is it possible to process local shapefile directly as a input data?
I don't think it's possible to use a shapefile as-is.
If the file is local to GeoServer (you tagged it, I assume that's what you are using), you can try to use a "file:///path/to/zipped/shapefile.zip" reference.
If the file is remote, you will have to zip it and add it to the request as a base64 encoded payload, or reference to it via HTTP (if you can zip it, and make it available on a web server that GeoServer can download from).