1) Install Alexa toolbar into your browser
This can improve, as Alexa panel consist from add-in toolbars  (and more ). using the plugin in your browsers can get you counts. every visitor coming to your webpage with the toolbar installed, will also count.

2) Install Alexa Widget 
Will a widget help you ? not according to Alexa.
Even so, I do recommend installing it , as there were bloggers showing improvement by using it and this a small thing you can do.

3) Write fresh high quality content
Maybe my best advice for you. content, content, content!
yes, this what can help you most to get more visitors, sales, better ranking and higher Alexa rank. Good content is what both users and search engines are looking for.

4) Write Original and engaging content 
Engaging content is something that motivates people to do something with it. if you write that you’re giving free ebook in your website and someone liked it, most changes he want to share it with a friend. that is engagement.
something that people need and seeking all the time.

5) Have relevant sites link to your website 
Put it simple, backlinks. you want to have relevant, industry links pointing to you.
That’s one sign telling search engines how good your site isthat’s mean you have something.

6) Use driving traffic keywords
Shortly ,What is called on page seo. improve the keywords and optimize them on the page.

7) Buy Alexa Traffic 
If you want to improve you rank shortly- buy traffic. but, as you stop it- expect to return soon to your original rank.

8) Have better SEO optimization

Work on all factors that matter to search engines like: speed, mobile, keywords, etc.