<template>
  .... your HTML
</template>

<script>
export default {
  data: () => ({
    ......data of your component
  }),
  mounted() {
    let recaptchaScript = document.createElement('script')
    recaptchaScript.setAttribute('src', 'https://www.google.com/recaptcha/api.js')
    document.head.appendChild(recaptchaScript)
  },
  methods: {
    ......methods of your component
  }
}
</script>