Yes, you can install StatCounter on your OpenScholar site. Here are the steps:
1. Sign up for a StatCounter account on StatCounter.com (they have a free account)
2. Add a new project
3. Enter your OpenScholar homepage (Front page) url -the project name can be the same as the url
4. Use the StatCounter Code for Default Guide to generate the Snippet to put into your OpenScholar page
5. Copy that code snippet and go to your OpenScholar Layout (Admin Bar > Appearance > Layout)
6. Click on Add New Widget and choose Embed Media, give the widget a name
7. Click on Choose File button, click on the Embed from Web tab, and paste in the StatCounter code snippet
8. Click Save and drag and drop the widget into a sidebar
9. Save the Front page layout and reload your front page, you should now see a counter
Now you can go back to StatCounter.com and view your project (the verification may or may not work, if you get an error just skip the verification/test setup step). Click on the project name to see how many people visited your site and who is visiting your site. To see where your visitors are coming from, click on the Country/State/City/ISP link on the left or Recent Visitor Map.
*Note: You might have to place the widget with the StatCounter code in your sidebar of your page for StatCounter to register the hits to the page.
*Note: If you want the counter to be invisible, please see StatCounter's FAQ on the topic: http://statcounter.com/support/knowledge-base/44/?search_text=invisible+counter