To get Google Analytics site statistics on your website powered by WordPress.com, you will need to upgrade to the Business plan.
Here’s how it’s stated at this WordPress.com support article about Google Analytics:
Google Analytics support on WordPress.com is available as a feature of the WordPress.com Business plan. Visit Settings → Traffic under My Sites to enable Google Analytics.
If you paid for the right upgrade, you’ll be able to see a screen that looks something like this:
Is the answer yes or no for using Google Analytics on WordPress.com?
To say it more bluntly, you can’t use Google Analytics with the default free plan on WordPress.com and it is not available on the Personal or Premium plan either. Saying it plainly and directly is more clear, right?
In other words, to use Google Analytics with WordPress.com, whether a site or blog, you would have to pay for the upgrade to a Business plan.
That WordPress.com support article adds:
WordPress.com has built-in stats tracking with reports that offer quick, at-a-glance views of the traffic on your site. New posts, likes and comments are shown alongside visitor activity, so it’s easier to make sense of the numbers.
Most of us don’t need to be overwhelmed with tons of data and statistics. WordPress.com built-in statistics should be sufficient in a majority of use cases.