If you are using yarn then put this command

yarn add @fortawesome/fontawesome-free

or

If you are using npm then put this command

yarn add @fortawesome/fontawesome-free

and add @import '@fortawesome/fontawesome-free/css/all.css'; this in app.scss file

or add import '@fortawesome/fontawesome-free/css/all.css'; in app.js file

Make sure to have the .css extension, otherwise the import will fail.

As a reminder:

Install @fortawesome/fontawesome-free (with npm or yarn depending on what package manager your project uses).

Then in your main.js you can just import all.css as per the example below

import Vue from 'vue'
import App from './App.vue'

import '@fortawesome/fontawesome-free/css/all.css'

Vue.config.productionTip = false

new Vue({
  render: h => h(App),
}).$mount('#app')

This will allow you to use the fa classes in regular HTML tags. I also recommend taking a look at the Vue supported library for FontAwesome here if you want to have more granularity with your imports. https://github.com/FortAwesome/vue-fontawesome

I simply solve the error by uninstall the googlefonts then again reinstall the google fonts by using following command.In my case I am using yarn so I use

yarn add @fortawesome/fontawesome-free

But in case of user that are using npm they should use following command

npm install --save @fortawesome/fontawesome-free

Also the following link is helpful google solve links for Npm and Yarn

: https://www.google.com/search?q=font%20awesome%20add%20by%20yaRN&oq=font%20awesome%20add%20by%20yaRN&aqs=chrome..69i57j33i10i160.11903j0j7&sourceid=chrome&ie=UTF-8