Add class to "link to content" view field
Along with Wims suggestion, I would suggest (as I usually do) to bypass fields in views, and render the view mode of the entity in question. Usually, this is sufficient in most cases if this is a presentation based view, and not a 'report' style view (where records are in table format and fields serve as cell data).

Then, supply the twig template for view modes, where the title is linked, and you can add the class(es) there. Now when you use that view mode to render in Views, it uses one template and is consistent, and Views that rely on rendering entities become easier to maintain and quicker to setup.

Here is an article that explains the difference and the benefit: https://www.amazeelabs.com/en/blog/views-field-rewriting-to-views-modes

That said, no, links themselves do not have a twig file (where you would see the anchor tag markup). I have seen the |merge option before that Wim linked to, though I have been unsuccessful in getting that to work in 8.2.5.

You could also implement theme_preprocess_field and supply the class to the attributes before it is rendered, though as you can imagine, if you have a lot of these, it'll be some work.