# config/routes.rb
resources :tags do
  get :autocomplete, on: :collection
end

# app/controllers/tags_controller.rb
def autocomplete
  @tags = ActsAsTaggableOn::Tag.where("name LIKE ?", "%#{params[:term]}%")
  render json: @tags.map(&:name)
end

// app/assets/javascripts/application.js
//= require jquery
//= require jquery-ui
//= require jquery_ujs
//= require autocomplete-rails

$(document).ready(function() {
  $('#tag_input').autocomplete({
    source: '/tags/autocomplete',
    minLength: 2
  });
});

# app/models/article.rb
class Article < ApplicationRecord
  acts_as_taggable_on :tags
end

<!-- app/views/articles/_form.html.erb -->
<%= form_for @article do |f| %>
  <div class="field">
    <%= f.label :tag_list, "Tags" %>
    <%= f.text_field :tag_list, data: { autocomplete_source: tags_autocomplete_path } %>
  </div>
  <%= f.submit %>
<% end %>

// app/assets/javascripts/articles.js
$(function() {
  $('#article_tag_list').autocomplete({
    source: $('#article_tag_list').data('autocomplete-source'),
    select: function(event, ui) {
      var terms = this.value.split(/,\s*/);
      terms.pop();
      terms.push(ui.item.value);
      terms.push("");
      this.value = terms.join(", ");
      return false;
    }
  });
});