You can use notes to keep track of when a tag is applied to a contact.
Simply create an automation with the “Tag is added” start trigger and the “Add note” action. Now, a note will appear as a time-stamped action in the activity stream on a contact’s record whenever the specified tag is applied:

For step-by-step instructions, read this Help article.
For more on tracking your tags, read our guide to using naming conventions to stay organized.