If you want to append this css file to header you can do it using mounted() function of the vue file. See the example.
Note: Assume you can access the css file as http://www.yoursite/assets/styles/vendor.css in the browser.
mounted() {
let style = document.createElement('link');
style.type = "text/css";
style.rel = "stylesheet";
style.href = '/assets/styles/vendor.css';
document.head.appendChild(style);
}