Verify your site Authorship
Must Read:- How To Claim And Verify Your Site in Alexa.
Install Alexa Toolbar and Status Bar
Put Alexa Widget On Your Site
Improve Your SEO Performance
Increase Your Site Traffic
Increase Your Reputation Links
Reputation links means how many numbers of sites are back linking to your site. Try to increase your site back links by leaving comments on other website or blogs which are popular and relevant to your content also. Try to leave your site link with no-follow or do-follow which you want. But keep in mind that backlinks should be leave on niche sites. If you have Bad linking this will have some bad effects in ranking and seo performance also.
Increase Site Reviews On Alexa
This is very important method to show your site popularity in alexa. Try to increase your alexa reviews ask your site users to leave reviews and comment on your ranking audit. It is better to encourage your site traffic to also rate your site on alexa to show what is their experience from your site or blog.