No, there's no API route that gives you a user's tag specific reputation information.  The [/users/{ids}/tags](https://api.stackexchange.com/docs/tags-on-users#order=desc&sort=popular&ids=1288&filter=default&site=stackoverflow&run=true) route only returns the combined count of questions and answers that a user has posted in a tag, but not the reputation information that you can get on the [user profile tags tab][1].  (Note: There's an app at [Badge Status for a particular Tag in Stackoverflow](https://stackapps.com/q/3527/9) that scrapes that page to get the information you're looking for.)


  [1]: http://stackoverflow.com/users/1288/bill-the-lizard?tab=tags