Alexa rank depends on page views and number of visitors / day.
if you want to rank your website very quickly, index your website with fast indexing plugin in scrapbox + do social sharing (fb, twitter, etc).
If you want to increase your Alexa, just focus on the site content and On page-SEO and your Alexa will improve eventually and Keep engaging users by posting new articles and share it on social media sites.
Most SEO specialists don't really mind Alexa rank. It depends on the page views and your visitors in a day. In order get high Alexa rank, you need to post quality content regularly and focus on On page SEO.