If your theme adheres to WordPress standards the menu is generated with a call to wp_nav_menu
. This function has a filter that allows you to modify the html. Like this:
add_filter ('wp_nav_menu', 'wpse312466_add_loginlink');
function wpse312466_add_loginlink ($nav_menu, $args) {
$nav_menu = '<div id="loglink"><a href="https://wordpress.stackexchange.com/link/to/loginpage">Login here</a></div>' . $nav_link
return $nav_menu
}
Now it depends on your css skills to get that link in the place where you want it to be.
The obvious place to stick this code is in a child theme, but you could also make it into a plugin.