A simple WordPress sidebar widget for searching in blog`s domain by Google. 
Uses JavaScript.

WordPress Google Search

saucecode

This plugin lets you know the ranking of your website in Google search result provided with keywords. You can define which country’s Google domain you would like to search as Google search result is different by country.
Keep monitor your website in the best ranking by using this plugin.
Search result ranking appears in this plugin is not take into account of:-
<ol>
<li>Search History: A user’s search results page can vary depending on what websites they’ve visited before. </li>
<li>Geography/Local Results: Google will show different results depending on the current location of an individual and where they live. </li>
<li>Social Media: Preference will be given to the endorsement of friends from social media such as Facebook, Google+ and etc. </li>
<li>Device: SERPs can vary depending on the device you are using to search.</li>
</ol>

SC Google Ranking

Get the ranking of your site in Google search engine provided with keywords

WordPress Google Search vs SC Google Ranking