Yes, using an Alexa widget like this you can display your site's Alexa rank on your site:


Just change yoursite.com to your website in two places in the HTML snippet below, and then copy and paste it into your website's HTML:
<a href="http://www.alexa.com/siteinfo/yoursite.com"><script type="text/javascript" src="http://xslt.alexa.com/site_stats/js/t/a?url=yoursite.com"></script></a>
Here is a widget that displays both your site's Alexa rank and Sites Linking In count:

<a href="http://www.alexa.com/siteinfo/yoursite.com"><script type="text/javascript" src="http://xslt.alexa.com/site_stats/js/s/a?url=yoursite.com"></script></a>