npm install --save @fortawesome/vue-fontawesome @fortawesome/fontawesome-svg-core @fortawesome/free-solid-svg-icons @fortawesome/free-brands-svg-icons

yarn add @fortawesome/vue-fontawesome @fortawesome/fontawesome-svg-core @fortawesome/free-solid-svg-icons @fortawesome/free-brands-svg-icons

create a fontawesome.js file in plugins folder and put this in it:

import Vue from 'vue'
import { library, config } from '@fortawesome/fontawesome-svg-core'
import { FontAwesomeIcon } from '@fortawesome/vue-fontawesome'
import { fas } from '@fortawesome/free-solid-svg-icons'
import { fab } from '@fortawesome/free-brands-svg-icons'

// This is important, we are going to let Nuxt.js worry about the CSS
config.autoAddCss = false

// You can add your icons directly in this plugin. See other examples for how you
// can add other styles or just individual icons.
library.add(fas)
library.add(fab)

// Register the component globally
Vue.component('font-awesome-icon', FontAwesomeIcon)

then in nuxt.config.js

 css: [
    '@fortawesome/fontawesome-svg-core/styles.css'
  ],

  /*
  ** Plugins to load before mounting the App
  */
  plugins: [
    '~/plugins/fontawesome.js',

  ],
  

and then to use in any page:

<font-awesome-icon icon="['fab', 'facebook']"  style="font-size: 22px"/>