While you can put a custom site google websearch on your site and you can put a button for +1, I do not believe there is a such thing as a google plus site search for sites. Think of google plus as google's version of facebook with search engine +1's.
Hope this helps.
Paul's right, the +1 button really is just to post the page to their version of Facebook. If you want to do a site search function to your site, you need to do it through google's site search at this page: http://www.google.com/sitesearch/