How do I access the Twitter API from my site to display my latest tweet?

Background:

I am using a reactive template to create a personal website and I would like to show my latest tweet in the footer. I don't need an embedded map, just the tweet itself (similar to the Momentum extension ).

This seems to be what I'm looking for: https://dev.twitter.com/rest/reference/get/statuses/user_timeline

Question:

How is my site supposed to authenticate with the Twitter API, disregarding the authentication credentials on the site's codebase?

Should I have an app in the middle that handles requests, or is it possible that my website can directly receive my latest tweet every time a user accesses my page?

thank